LMFDB - Embedded newform 798.2.bu.b.611.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(53,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 12, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.53"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bu (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			611.7
Character	$\chi$	$=$	798.611
Dual form			798.2.bu.b.431.7

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 - 0.342020i) q^{2} +(-1.13904 - 1.30483i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.125326 + 0.149358i) q^{5} +(-1.51663 - 0.836567i) q^{6} +(-2.61695 + 0.389293i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.405175 + 2.97251i) q^{9} +(-0.0666847 + 0.183215i) q^{10} +5.11456i q^{11} +(-1.71129 - 0.267399i) q^{12} +(-1.65749 + 4.55391i) q^{13} +(-2.32599 + 1.26087i) q^{14} +(0.337639 - 0.00659504i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-6.93439 - 1.22272i) q^{17} +(0.635920 + 2.93183i) q^{18} +(2.45626 + 3.60094i) q^{19} +0.194973i q^{20} +(3.48878 + 2.97127i) q^{21} +(1.74928 + 4.80612i) q^{22} +(2.96273 - 8.14004i) q^{23} +(-1.69954 + 0.334022i) q^{24} +(0.861640 + 4.88660i) q^{25} +4.84617i q^{26} +(4.34014 - 2.85713i) q^{27} +(-1.75447 + 1.98036i) q^{28} +(1.51822 - 1.27394i) q^{29} +(0.315021 - 0.121677i) q^{30} +(-0.417293 - 0.240924i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(6.67364 - 5.82569i) q^{33} +(-6.93439 + 1.22272i) q^{34} +(0.269829 - 0.439652i) q^{35} +(1.60031 + 2.53752i) q^{36} +(-0.661000 - 0.381628i) q^{37} +(3.53972 + 2.54369i) q^{38} +(7.83003 - 3.02434i) q^{39} +(0.0666847 + 0.183215i) q^{40} +(-8.40841 + 3.06041i) q^{41} +(4.29461 + 1.59885i) q^{42} +(-1.13707 + 6.44867i) q^{43} +(3.28758 + 3.91798i) q^{44} +(-0.393190 - 0.433050i) q^{45} -8.66245i q^{46} +(0.803487 - 0.141676i) q^{47} +(-1.48280 + 0.895154i) q^{48} +(6.69690 - 2.03752i) q^{49} +(2.48099 + 4.29721i) q^{50} +(6.30310 + 10.4409i) q^{51} +(1.65749 + 4.55391i) q^{52} +(-1.92966 + 1.61918i) q^{53} +(3.10120 - 4.16924i) q^{54} +(-0.763901 - 0.640989i) q^{55} +(-0.971340 + 2.46100i) q^{56} +(1.90085 - 7.30663i) q^{57} +(0.990946 - 1.71637i) q^{58} +(-1.11159 + 6.30412i) q^{59} +(0.254407 - 0.222082i) q^{60} +(-9.59315 - 3.49162i) q^{61} +(-0.474528 - 0.0836721i) q^{62} +(-0.0968538 - 7.93666i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.472436 - 0.818283i) q^{65} +(4.27867 - 7.75688i) q^{66} +(0.460499 - 1.26521i) q^{67} +(-6.09800 + 3.52068i) q^{68} +(-13.9961 + 5.40597i) q^{69} +(0.103187 - 0.505425i) q^{70} +(-2.09330 + 11.8717i) q^{71} +(2.37168 + 1.83715i) q^{72} +(-2.32863 - 1.95396i) q^{73} +(-0.751661 - 0.132538i) q^{74} +(5.39475 - 6.69033i) q^{75} +(4.19625 + 1.17963i) q^{76} +(-1.99106 - 13.3846i) q^{77} +(6.32344 - 5.51998i) q^{78} +(-4.19022 - 0.738849i) q^{79} +(0.125326 + 0.149358i) q^{80} +(-8.67167 - 2.40877i) q^{81} +(-6.85460 + 5.75169i) q^{82} +(5.01312 - 2.89433i) q^{83} +(4.58245 + 0.0335791i) q^{84} +(1.05168 - 0.882468i) q^{85} +(1.13707 + 6.44867i) q^{86} +(-3.39158 - 0.529955i) q^{87} +(4.42934 + 2.55728i) q^{88} +(0.721959 - 0.605795i) q^{89} +(-0.517589 - 0.272455i) q^{90} +(2.56477 - 12.5626i) q^{91} +(-2.96273 - 8.14004i) q^{92} +(0.160948 + 0.818920i) q^{93} +(0.706575 - 0.407941i) q^{94} +(-0.845663 - 0.0844309i) q^{95} +(-1.08722 + 1.34832i) q^{96} +(-2.63474 + 3.13996i) q^{97} +(5.59616 - 4.20512i) q^{98} +(-15.2031 - 2.07229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 81 q^{8} + 15 q^{13} - 6 q^{14} + 3 q^{15} + 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} + 9 q^{27} + 9 q^{28} - 6 q^{29} + 24 q^{33} + 6 q^{34} - 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots + 39 q^{99}+O(q^{100}) $ 162 * q + 81 * q^8 + 15 * q^13 - 6 * q^14 + 3 * q^15 + 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 + 9 * q^27 + 9 * q^28 - 6 * q^29 + 24 * q^33 + 6 * q^34 - 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 + 12 * q^44 + 45 * q^45 - 12 * q^47 - 48 * q^49 - 87 * q^50 + 24 * q^51 - 15 * q^52 + 18 * q^54 - 18 * q^57 + 48 * q^59 + 18 * q^60 + 45 * q^61 - 36 * q^62 - 21 * q^63 - 81 * q^64 - 36 * q^65 + 12 * q^66 + 9 * q^67 - 9 * q^69 - 24 * q^70 - 12 * q^71 + 102 * q^73 - 39 * q^74 - 18 * q^78 - 42 * q^79 - 12 * q^81 + 57 * q^84 - 6 * q^85 + 9 * q^86 + 60 * q^87 - 54 * q^89 + 12 * q^90 - 18 * q^91 + 105 * q^93 - 72 * q^94 - 12 * q^97 + 27 * q^98 + 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−1.13904	−	1.30483i	−0.657625	−	0.753345i
$3$	−1.13904	−	1.30483i	−0.657625	−	0.753345i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.125326	+	0.149358i	−0.0560476	+	0.0667949i	−0.793340	−	0.608779i	$-0.791660\pi$
$5$	−0.125326	+	0.149358i	−0.0560476	+	0.0667949i	0.737292	+	0.675574i	$0.236104\pi$
$6$	−1.51663	−	0.836567i	−0.619160	−	0.341527i
$7$	−2.61695	+	0.389293i	−0.989116	+	0.147139i
$7$	−2.61695	+	0.389293i	−0.989116	+	0.147139i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.405175	+	2.97251i	−0.135058	+	0.990838i
$10$	−0.0666847	+	0.183215i	−0.0210876	+	0.0579376i
$11$			5.11456i			1.54210i	0.636776	+	0.771049i	$0.280268\pi$
$11$			5.11456i			1.54210i	−0.636776	+	0.771049i	$0.719732\pi$
$12$	−1.71129	−	0.267399i	−0.494006	−	0.0771913i
$13$	−1.65749	+	4.55391i	−0.459704	+	1.26303i	0.466002	+	0.884784i	$0.345694\pi$
$13$	−1.65749	+	4.55391i	−0.459704	+	1.26303i	−0.925706	+	0.378243i	$0.876528\pi$
$14$	−2.32599	+	1.26087i	−0.621646	+	0.336981i
$15$	0.337639	−	0.00659504i	0.0871780	−	0.00170283i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−6.93439	−	1.22272i	−1.68184	−	0.296553i	−0.750543	−	0.660822i	$-0.770208\pi$
$17$	−6.93439	−	1.22272i	−1.68184	−	0.296553i	−0.931294	+	0.364269i	$0.881319\pi$
$18$	0.635920	+	2.93183i	0.149888	+	0.691038i
$19$	2.45626	+	3.60094i	0.563504	+	0.826113i
$19$	2.45626	+	3.60094i	0.563504	+	0.826113i
$20$			0.194973i			0.0435973i
$21$	3.48878	+	2.97127i	0.761314	+	0.648384i
$22$	1.74928	+	4.80612i	0.372948	+	1.02467i
$23$	2.96273	−	8.14004i	0.617773	−	1.69732i	−0.0946007	−	0.995515i	$-0.530157\pi$
$23$	2.96273	−	8.14004i	0.617773	−	1.69732i	0.712373	−	0.701801i	$-0.247620\pi$
$24$	−1.69954	+	0.334022i	−0.346917	+	0.0681819i
$25$	0.861640	+	4.88660i	0.172328	+	0.977320i
$26$			4.84617i			0.950412i
$27$	4.34014	−	2.85713i	0.835261	−	0.549854i
$28$	−1.75447	+	1.98036i	−0.331564	+	0.374253i
$29$	1.51822	−	1.27394i	0.281926	−	0.236564i	−0.490848	−	0.871245i	$-0.663313\pi$
$29$	1.51822	−	1.27394i	0.281926	−	0.236564i	0.772774	+	0.634681i	$0.218869\pi$
$30$	0.315021	−	0.121677i	0.0575147	−	0.0222150i
$31$	−0.417293	−	0.240924i	−0.0749480	−	0.0432713i	0.462058	−	0.886850i	$-0.347111\pi$
$31$	−0.417293	−	0.240924i	−0.0749480	−	0.0432713i	−0.537006	+	0.843579i	$0.680445\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	6.67364	−	5.82569i	1.16173	−	1.01412i
$34$	−6.93439	+	1.22272i	−1.18924	+	0.209695i
$35$	0.269829	−	0.439652i	0.0456095	−	0.0743147i
$36$	1.60031	+	2.53752i	0.266719	+	0.422920i
$37$	−0.661000	−	0.381628i	−0.108668	−	0.0627393i	0.444681	−	0.895689i	$-0.353317\pi$
$37$	−0.661000	−	0.381628i	−0.108668	−	0.0627393i	−0.553349	+	0.832950i	$0.686650\pi$
$38$	3.53972	+	2.54369i	0.574219	+	0.412641i
$39$	7.83003	−	3.02434i	1.25381	−	0.484282i
$40$	0.0666847	+	0.183215i	0.0105438	+	0.0289688i
$41$	−8.40841	+	3.06041i	−1.31317	+	0.477956i	−0.901265	−	0.433269i	$-0.857360\pi$
$41$	−8.40841	+	3.06041i	−1.31317	+	0.477956i	−0.411909	+	0.911225i	$0.635138\pi$
$42$	4.29461	+	1.59885i	0.662673	+	0.246707i
$43$	−1.13707	+	6.44867i	−0.173402	+	0.983412i	0.766570	+	0.642161i	$0.221962\pi$
$43$	−1.13707	+	6.44867i	−0.173402	+	0.983412i	−0.939972	+	0.341251i	$0.889149\pi$
$44$	3.28758	+	3.91798i	0.495621	+	0.590658i
$45$	−0.393190	−	0.433050i	−0.0586133	−	0.0645553i
$46$		−	8.66245i		−	1.27721i
$47$	0.803487	−	0.141676i	0.117201	−	0.0206656i	−0.114740	−	0.993396i	$-0.536604\pi$
$47$	0.803487	−	0.141676i	0.117201	−	0.0206656i	0.231941	+	0.972730i	$0.425492\pi$
$48$	−1.48280	+	0.895154i	−0.214024	+	0.129204i
$49$	6.69690	−	2.03752i	0.956700	−	0.291075i
$50$	2.48099	+	4.29721i	0.350865	+	0.607717i
$51$	6.30310	+	10.4409i	0.882611	+	1.46202i
$52$	1.65749	+	4.55391i	0.229852	+	0.631514i
$53$	−1.92966	+	1.61918i	−0.265059	+	0.222411i	−0.765625	−	0.643288i	$-0.777570\pi$
$53$	−1.92966	+	1.61918i	−0.265059	+	0.222411i	0.500565	+	0.865699i	$0.333126\pi$
$54$	3.10120	−	4.16924i	0.422020	−	0.567361i
$55$	−0.763901	−	0.640989i	−0.103004	−	0.0864309i
$56$	−0.971340	+	2.46100i	−0.129801	+	0.328864i
$57$	1.90085	−	7.30663i	0.251774	−	0.967786i
$58$	0.990946	−	1.71637i	0.130118	−	0.225370i
$59$	−1.11159	+	6.30412i	−0.144716	+	0.820727i	0.822878	+	0.568218i	$0.192367\pi$
$59$	−1.11159	+	6.30412i	−0.144716	+	0.820727i	−0.967595	+	0.252509i	$0.918744\pi$
$60$	0.254407	−	0.222082i	0.0328438	−	0.0286707i
$61$	−9.59315	−	3.49162i	−1.22828	−	0.447056i	−0.355270	−	0.934764i	$-0.615611\pi$
$61$	−9.59315	−	3.49162i	−1.22828	−	0.447056i	−0.873007	+	0.487707i	$0.837833\pi$
$62$	−0.474528	−	0.0836721i	−0.0602651	−	0.0106264i
$63$	−0.0968538	−	7.93666i	−0.0122024	−	0.999926i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.472436	−	0.818283i	−0.0585985	−	0.101496i
$66$	4.27867	−	7.75688i	0.526668	−	0.954806i
$67$	0.460499	−	1.26521i	0.0562589	−	0.154570i	−0.908380	−	0.418147i	$-0.862680\pi$
$67$	0.460499	−	1.26521i	0.0562589	−	0.154570i	0.964639	+	0.263576i	$0.0849021\pi$
$68$	−6.09800	+	3.52068i	−0.739491	+	0.426945i
$69$	−13.9961	+	5.40597i	−1.68493	+	0.650802i
$70$	0.103187	−	0.505425i	0.0123332	−	0.0604098i
$71$	−2.09330	+	11.8717i	−0.248429	+	1.40891i	0.563963	+	0.825800i	$0.309276\pi$
$71$	−2.09330	+	11.8717i	−0.248429	+	1.40891i	−0.812392	+	0.583112i	$0.801835\pi$
$72$	2.37168	+	1.83715i	0.279506	+	0.216510i
$73$	−2.32863	−	1.95396i	−0.272546	−	0.228693i	0.496262	−	0.868173i	$-0.334705\pi$
$73$	−2.32863	−	1.95396i	−0.272546	−	0.228693i	−0.768808	+	0.639480i	$0.779150\pi$
$74$	−0.751661	−	0.132538i	−0.0873788	−	0.0154072i
$75$	5.39475	−	6.69033i	0.622932	−	0.772533i
$76$	4.19625	+	1.17963i	0.481342	+	0.135313i
$77$	−1.99106	−	13.3846i	−0.226902	−	1.52531i
$78$	6.32344	−	5.51998i	0.715988	−	0.625015i
$79$	−4.19022	−	0.738849i	−0.471436	−	0.0831270i	−0.0671176	−	0.997745i	$-0.521380\pi$
$79$	−4.19022	−	0.738849i	−0.471436	−	0.0831270i	−0.404319	+	0.914618i	$0.632491\pi$
$80$	0.125326	+	0.149358i	0.0140119	+	0.0166987i
$81$	−8.67167	−	2.40877i	−0.963519	−	0.267642i
$82$	−6.85460	+	5.75169i	−0.756964	+	0.635168i
$83$	5.01312	−	2.89433i	0.550261	−	0.317694i	−0.198966	−	0.980006i	$-0.563758\pi$
$83$	5.01312	−	2.89433i	0.550261	−	0.317694i	0.749227	+	0.662313i	$0.230425\pi$
$84$	4.58245	+	0.0335791i	0.499987	+	0.00366378i
$85$	1.05168	−	0.882468i	0.114071	−	0.0957171i
$86$	1.13707	+	6.44867i	0.122614	+	0.695377i
$87$	−3.39158	−	0.529955i	−0.363616	−	0.0568172i
$88$	4.42934	+	2.55728i	0.472169	+	0.272607i
$89$	0.721959	−	0.605795i	0.0765275	−	0.0642142i	−0.603722	−	0.797195i	$-0.706316\pi$
$89$	0.721959	−	0.605795i	0.0765275	−	0.0642142i	0.680249	+	0.732981i	$0.261872\pi$
$90$	−0.517589	−	0.272455i	−0.0545587	−	0.0287193i
$91$	2.56477	−	12.5626i	0.268860	−	1.31692i
$92$	−2.96273	−	8.14004i	−0.308886	−	0.848658i
$93$	0.160948	+	0.818920i	0.0166895	+	0.0849180i
$94$	0.706575	−	0.407941i	0.0728776	−	0.0420759i
$95$	−0.845663	−	0.0844309i	−0.0867632	−	0.00866242i
$96$	−1.08722	+	1.34832i	−0.110964	+	0.137612i
$97$	−2.63474	+	3.13996i	−0.267517	+	0.318815i	−0.883034	−	0.469309i	$-0.844503\pi$
$97$	−2.63474	+	3.13996i	−0.267517	+	0.318815i	0.615516	+	0.788124i	$0.288947\pi$
$98$	5.59616	−	4.20512i	0.565297	−	0.424781i
$99$	−15.2031	−	2.07229i	−1.52797	−	0.208273i
$100$	3.80110	+	3.18950i	0.380110	+	0.318950i
$101$	−3.42087	+	0.603191i	−0.340389	+	0.0600198i	−0.341230	−	0.939980i	$-0.610843\pi$
$101$	−3.42087	+	0.603191i	−0.340389	+	0.0600198i	0.000840872		1.00000i	$0.499732\pi$
$102$	9.49399	+	7.65549i	0.940045	+	0.758006i
$103$	12.1418	−	7.01008i	1.19637	−	0.690723i	0.236624	−	0.971601i	$-0.423959\pi$
$103$	12.1418	−	7.01008i	1.19637	−	0.690723i	0.959744	+	0.280878i	$0.0906256\pi$
$104$	3.11506	+	3.71238i	0.305456	+	0.364029i
$105$	−0.881018	+	0.148699i	−0.0859786	+	0.0145116i
$106$	−1.25950	+	2.18151i	−0.122333	+	0.211887i
$107$	11.3079			1.09318			0.546588	−	0.837401i	$-0.315926\pi$
$107$	11.3079			1.09318			0.546588	+	0.837401i	$0.315926\pi$
$108$	1.48822	−	4.97848i	0.143204	−	0.479054i
$109$	6.84634	+	18.8102i	0.655760	+	1.80169i	0.595283	+	0.803516i	$0.297040\pi$
$109$	6.84634	+	18.8102i	0.655760	+	1.80169i	0.0604775	+	0.998170i	$0.480738\pi$
$110$	−0.937063	−	0.341063i	−0.0893455	−	0.0325191i
$111$	0.254944	+	1.29718i	0.0241982	+	0.123123i
$112$	−0.0710510	+	2.64480i	−0.00671369	+	0.249910i
$113$	−12.0260			−1.13131			−0.565656	−	0.824642i	$-0.691377\pi$
$113$	−12.0260			−1.13131			−0.565656	+	0.824642i	$0.691377\pi$
$114$	−0.712798	−	7.51611i	−0.0667597	−	0.703948i
$115$	0.844472	+	1.46267i	0.0787475	+	0.136395i
$116$	0.344152	−	1.95178i	0.0319537	−	0.181218i
$117$	−12.8650	−	6.77203i	−1.18937	−	0.626074i
$118$	1.11159	+	6.30412i	0.102330	+	0.580342i
$119$	18.6230	+	0.500296i	1.70717	+	0.0458620i
$120$	0.163108	−	0.295701i	0.0148896	−	0.0269937i
$121$	−15.1587			−1.37807
$122$	−10.2088			−0.924263
$123$	13.5708	+	7.48563i	1.22364	+	0.674957i
$124$	−0.474528	+	0.0836721i	−0.0426139	+	0.00751398i
$125$	−1.68210	−	0.971159i	−0.150451	−	0.0868631i
$126$	−2.80551	−	7.42490i	−0.249935	−	0.661462i
$127$	1.96992	−	5.41231i	0.174802	−	0.480265i	−0.821091	−	0.570797i	$-0.806634\pi$
$127$	1.96992	−	5.41231i	0.174802	−	0.480265i	0.995894	+	0.0905318i	$0.0288567\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	9.70960	−	5.86160i	0.854883	−	0.516085i
$130$	−0.723814	−	0.607352i	−0.0634827	−	0.0532683i
$131$	−2.20917	−	6.06965i	−0.193016	−	0.530308i	0.804999	−	0.593276i	$-0.202166\pi$
$131$	−2.20917	−	6.06965i	−0.193016	−	0.530308i	−0.998016	+	0.0629679i	$0.979943\pi$
$132$	1.36763	−	8.75247i	0.119037	−	0.761805i
$133$	−7.82974	−	8.46730i	−0.678924	−	0.734208i
$134$		−	1.34641i		−	0.116312i
$135$	−0.117199	+	1.00631i	−0.0100869	+	0.0866092i
$136$	−4.52610	+	5.39400i	−0.388110	+	0.462531i
$137$	5.25705	+	6.26511i	0.449140	+	0.535265i	0.942342	−	0.334650i	$-0.108618\pi$
$137$	5.25705	+	6.26511i	0.449140	+	0.535265i	−0.493202	+	0.869915i	$0.664174\pi$
$138$	−11.3030	+	9.86688i	−0.962179	+	0.839925i
$139$	−8.17595	−	2.97580i	−0.693475	−	0.252404i	−0.0288524	−	0.999584i	$-0.509185\pi$
$139$	−8.17595	−	2.97580i	−0.693475	−	0.252404i	−0.664622	+	0.747180i	$0.731407\pi$
$140$	−0.0759016	−	0.510236i	−0.00641485	−	0.0431228i
$141$	−1.10007	−	0.887041i	−0.0926424	−	0.0747023i
$142$	2.09330	+	11.8717i	0.175666	+	0.996251i
$143$	−23.2912	−	8.47732i	−1.94771	−	0.708909i
$144$	2.85700	+	0.915191i	0.238083	+	0.0762659i
$145$			0.386416i			0.0320901i
$146$	−2.85649	−	1.03968i	−0.236405	−	0.0860444i
$147$	−10.2867	−	6.41751i	−0.848430	−	0.529308i
$148$	−0.751661	+	0.132538i	−0.0617862	+	0.0108946i
$149$	−1.45444	−	0.256456i	−0.119152	−	0.0210097i	0.113754	−	0.993509i	$-0.463712\pi$
$149$	−1.45444	−	0.256456i	−0.119152	−	0.0210097i	−0.232906	+	0.972499i	$0.574823\pi$
$150$	2.78118	−	8.13197i	0.227083	−	0.663973i
$151$	8.85631	−	5.11319i	0.720716	−	0.416106i	−0.0943001	−	0.995544i	$-0.530061\pi$
$151$	8.85631	−	5.11319i	0.720716	−	0.416106i	0.815016	+	0.579438i	$0.196728\pi$
$152$	4.34664	−	0.326711i	0.352559	−	0.0264997i
$153$	6.44419	−	20.1171i	0.520982	−	1.62638i
$154$	−6.44878	−	11.8964i	−0.519657	−	0.958639i
$155$	0.0882817	−	0.0321319i	0.00709096	−	0.00258090i
$156$	4.05414	−	7.34983i	0.324591	−	0.588457i
$157$	13.8672	−	5.04724i	1.10672	−	0.402813i	0.276931	−	0.960890i	$-0.410683\pi$
$157$	13.8672	−	5.04724i	1.10672	−	0.402813i	0.829790	+	0.558076i	$0.188460\pi$
$158$	−4.19022	+	0.738849i	−0.333356	+	0.0587796i
$159$	4.31072	+	0.673575i	0.341862	+	0.0534180i
$160$	0.168852	+	0.0974865i	0.0133489	+	0.00770699i
$161$	−4.58448	+	22.4555i	−0.361308	+	1.76974i
$162$	−8.97255	+	0.702378i	−0.704950	+	0.0551840i
$163$	−4.51743	−	7.82442i	−0.353833	−	0.612856i	0.633085	−	0.774082i	$-0.281788\pi$
$163$	−4.51743	−	7.82442i	−0.353833	−	0.612856i	−0.986917	+	0.161226i	$0.948455\pi$
$164$	−4.47402	+	7.74923i	−0.349362	+	0.605114i
$165$	0.0337308	+	1.72687i	0.00262594	+	0.134437i
$166$	3.72087	−	4.43436i	0.288796	−	0.344173i
$167$	0.900701	+	5.10813i	0.0696983	+	0.395279i	0.999621	+	0.0275240i	$0.00876228\pi$
$167$	0.900701	+	5.10813i	0.0696983	+	0.395279i	−0.929923	+	0.367755i	$0.880127\pi$
$168$	4.31758	−	1.53574i	0.333109	−	0.118485i
$169$	−8.03224	−	6.73985i	−0.617865	−	0.518450i
$170$	0.686438	−	1.18895i	0.0526474	−	0.0911880i
$171$	−11.6991	+	5.84225i	−0.894650	+	0.446768i
$172$	3.27407	+	5.67086i	0.249646	+	0.432399i
$173$	−11.1054	+	4.04202i	−0.844325	+	0.307309i	−0.727725	−	0.685870i	$-0.759422\pi$
$173$	−11.1054	+	4.04202i	−0.844325	+	0.307309i	−0.116601	+	0.993179i	$0.537200\pi$
$174$	−3.36830	+	0.661995i	−0.255350	+	0.0501857i
$175$	−4.15719	−	12.4526i	−0.314254	−	0.941327i
$176$	5.03686	+	0.888134i	0.379668	+	0.0669456i
$177$	9.49197	−	5.73022i	0.713460	−	0.430709i
$178$	0.471225	−	0.816186i	0.0353198	−	0.0611757i
$179$	−21.3061			−1.59249			−0.796247	−	0.604972i	$-0.793184\pi$
$179$	−21.3061			−1.59249			−0.796247	+	0.604972i	$0.793184\pi$
$180$	−0.579560	−	0.0789981i	−0.0431978	−	0.00588817i
$181$	−6.62937	−	7.90058i	−0.492758	−	0.587246i	0.461159	−	0.887317i	$-0.347434\pi$
$181$	−6.62937	−	7.90058i	−0.492758	−	0.587246i	−0.953917	+	0.300072i	$0.902989\pi$
$182$	−1.88658	−	12.6822i	−0.139842	−	0.940067i
$183$	6.37100	+	16.4946i	0.470958	+	1.21931i
$184$	−5.56812	−	6.63582i	−0.410487	−	0.489199i
$185$	0.139840	−	0.0508976i	0.0102812	−	0.00374206i
$186$	0.431328	+	0.714485i	0.0316265	+	0.0523886i
$187$	6.25368	−	35.4664i	0.457314	−	2.59356i
$188$	0.524439	−	0.625002i	0.0382486	−	0.0455830i
$189$	−10.2457	+	9.16656i	−0.745265	+	0.666769i
$190$	−0.823541	+	0.209895i	−0.0597459	+	0.0152274i
$191$	14.0932	+	8.13673i	1.01975	+	0.588753i	0.914032	−	0.405643i	$-0.132952\pi$
$191$	14.0932	+	8.13673i	1.01975	+	0.588753i	0.105719	+	0.994396i	$0.466286\pi$
$192$	−0.560498	+	1.63885i	−0.0404504	+	0.118274i
$193$	−0.812633	+	0.968458i	−0.0584946	+	0.0697112i	−0.794498	−	0.607266i	$-0.792266\pi$
$193$	−0.812633	+	0.968458i	−0.0584946	+	0.0697112i	0.736004	+	0.676977i	$0.236711\pi$
$194$	−1.40192	+	3.85173i	−0.100652	+	0.276538i
$195$	−0.529599	+	1.54851i	−0.0379254	+	0.110891i
$196$	3.82043	−	5.86552i	0.272888	−	0.418966i
$197$	16.9368	−	9.77847i	1.20670	−	0.696687i	0.244661	−	0.969609i	$-0.421323\pi$
$197$	16.9368	−	9.77847i	1.20670	−	0.696687i	0.962036	+	0.272922i	$0.0879900\pi$
$198$	−14.9950	+	3.25245i	−1.06565	+	0.231142i
$199$	8.45050	+	3.07573i	0.599040	+	0.218033i	0.623701	−	0.781663i	$-0.285628\pi$
$199$	8.45050	+	3.07573i	0.599040	+	0.218033i	−0.0246609	+	0.999696i	$0.507851\pi$
$200$	4.66274	+	1.69710i	0.329706	+	0.120003i
$201$	−2.17542	+	0.840252i	−0.153442	+	0.0592668i
$202$	−3.00826	+	1.73682i	−0.211660	+	0.122202i
$203$	−3.47717	+	3.92486i	−0.244050	+	0.275471i
$204$	11.5398	+	3.94667i	0.807945	+	0.276322i
$205$	0.596698	−	1.63941i	0.0416752	−	0.114502i
$206$	9.01198	−	10.7401i	0.627894	−	0.748295i
$207$	22.9960	+	12.1049i	1.59833	+	0.841349i
$208$	4.19691	+	2.42308i	0.291003	+	0.168011i
$209$	−18.4172	+	12.5627i	−1.27395	+	0.868979i
$210$	−0.777028	+	0.441058i	−0.0536200	+	0.0304359i
$211$	12.2821	−	14.6373i	0.845537	−	1.00767i	−0.154270	−	0.988029i	$-0.549303\pi$
$211$	12.2821	−	14.6373i	0.845537	−	1.00767i	0.999807	−	0.0196427i	$-0.00625286\pi$
$212$	−0.437419	+	2.48072i	−0.0300420	+	0.170377i
$213$	17.8749	−	10.7909i	1.22477	−	0.739383i
$214$	10.6260	−	3.86753i	0.726375	−	0.264379i
$215$	−0.820655	−	0.978018i	−0.0559682	−	0.0667003i
$216$	−0.304274	−	5.18724i	−0.0207032	−	0.352947i
$217$	1.18583	+	0.468039i	0.0804992	+	0.0317725i
$218$	12.8669	+	15.3342i	0.871457	+	1.03856i
$219$	0.102823	+	5.26411i	0.00694813	+	0.355716i
$220$	−0.997202			−0.0672313
$221$	17.0618	−	29.5519i	1.14770	−	1.98788i
$222$	0.683232	+	1.13176i	0.0458555	+	0.0759586i
$223$	−18.7661	−	3.30896i	−1.25667	−	0.221585i	−0.494623	−	0.869108i	$-0.664694\pi$
$223$	−18.7661	−	3.30896i	−1.25667	−	0.221585i	−0.762046	+	0.647523i	$0.775805\pi$
$224$	0.837808	+	2.50960i	0.0559784	+	0.167680i
$225$	−14.8746	+	0.581308i	−0.991640	+	0.0387539i
$226$	−11.3007	+	4.11314i	−0.751715	+	0.273602i
$227$	8.79449	+	15.2325i	0.583711	+	1.01102i	0.995035	+	0.0995275i	$0.0317331\pi$
$227$	8.79449	+	15.2325i	0.583711	+	1.01102i	−0.411324	+	0.911489i	$0.634934\pi$
$228$	−3.24047	−	6.81904i	−0.214606	−	0.451602i
$229$	2.24551	−	3.88934i	0.148388	−	0.257015i	−0.782244	−	0.622972i	$-0.785925\pi$
$229$	2.24551	−	3.88934i	0.148388	−	0.257015i	0.930632	+	0.365957i	$0.119258\pi$
$230$	1.29381	+	1.08563i	0.0853111	+	0.0715845i
$231$	−15.1967	+	17.8436i	−0.999871	+	1.17402i
$232$	−0.344152	−	1.95178i	−0.0225947	−	0.128141i
$233$	−6.58401	+	7.84651i	−0.431333	+	0.514042i	−0.937306	−	0.348507i	$-0.886689\pi$
$233$	−6.58401	+	7.84651i	−0.431333	+	0.514042i	0.505974	+	0.862549i	$0.331133\pi$
$234$	−14.4053	−	1.96354i	−0.941704	−	0.128361i
$235$	−0.0795375	+	0.137763i	−0.00518846	+	0.00898667i
$236$	3.20069	+	5.54375i	0.208347	+	0.360868i
$237$	3.80875	+	6.30911i	0.247405	+	0.409821i
$238$	17.6710	−	5.89931i	1.14544	−	0.382395i
$239$	−18.7146	−	10.8049i	−1.21055	−	0.698911i	−0.247671	−	0.968844i	$-0.579665\pi$
$239$	−18.7146	−	10.8049i	−1.21055	−	0.698911i	−0.962879	+	0.269933i	$0.912998\pi$
$240$	0.0521355	−	0.333655i	0.00336533	−	0.0215373i
$241$	−0.203958	+	0.0359634i	−0.0131381	+	0.00231660i	−0.180213	−	0.983628i	$-0.557679\pi$
$241$	−0.203958	+	0.0359634i	−0.0131381	+	0.00231660i	0.167075	+	0.985944i	$0.446568\pi$
$242$	−14.2446	+	5.18459i	−0.915675	+	0.333278i
$243$	6.73433	+	14.0588i	0.432008	+	0.901870i
$244$	−9.59315	+	3.49162i	−0.614139	+	0.223528i
$245$	−0.534977	+	1.25559i	−0.0341785	+	0.0802168i
$246$	15.3127	+	2.39269i	0.976299	+	0.152553i
$247$	−20.4696	+	5.21706i	−1.30245	+	0.331954i
$248$	−0.417293	+	0.240924i	−0.0264981	+	0.0152987i
$249$	−9.48676	−	3.24453i	−0.601199	−	0.205614i
$250$	−1.91281	−	0.337280i	−0.120977	−	0.0213315i
$251$	26.2787	−	4.63365i	1.65870	−	0.292474i	0.735710	−	0.677297i	$-0.236849\pi$
$251$	26.2787	−	4.63365i	1.65870	−	0.292474i	0.922990	+	0.384824i	$0.125738\pi$
$252$	−5.17578	−	6.01758i	−0.326044	−	0.379072i
$253$	41.6327	+	15.1531i	2.61743	+	0.952666i
$254$		−	5.75966i		−	0.361393i
$255$	−2.34938	−	0.367105i	−0.147124	−	0.0229890i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	0.288988	+	1.63893i	0.0180266	+	0.102234i	0.992494	−	0.122297i	$-0.0390261\pi$
$257$	0.288988	+	1.63893i	0.0180266	+	0.102234i	−0.974467	+	0.224531i	$0.927915\pi$
$258$	7.11925	−	8.82898i	0.443225	−	0.549668i
$259$	1.87837	+	0.741382i	0.116716	+	0.0460672i
$260$	−0.887889	−	0.323165i	−0.0550646	−	0.0200419i
$261$	3.17165	+	5.02909i	0.196320	+	0.311293i
$262$	−4.15189	−	4.94802i	−0.256504	−	0.305690i
$263$	−6.33482	+	7.54955i	−0.390622	+	0.465525i	−0.925137	−	0.379634i	$-0.876050\pi$
$263$	−6.33482	+	7.54955i	−0.390622	+	0.465525i	0.534515	+	0.845159i	$0.320494\pi$
$264$	−1.70837	−	8.69239i	−0.105143	−	0.534980i
$265$		−	0.491136i		−	0.0301702i
$266$	−10.2535	−	5.27873i	−0.628685	−	0.323660i
$267$	−1.61280	−	0.252010i	−0.0987018	−	0.0154228i
$268$	−0.460499	−	1.26521i	−0.0281295	−	0.0772851i
$269$	5.39395	+	4.52606i	0.328875	+	0.275959i	0.792241	−	0.610208i	$-0.208914\pi$
$269$	5.39395	+	4.52606i	0.328875	+	0.275959i	−0.463366	+	0.886167i	$0.653359\pi$
$270$	0.234047	+	0.985705i	0.0142436	+	0.0599881i
$271$	21.3286	+	17.8968i	1.29562	+	1.08715i	0.990884	+	0.134716i	$0.0430123\pi$
$271$	21.3286	+	17.8968i	1.29562	+	1.08715i	0.304735	+	0.952437i	$0.401432\pi$
$272$	−2.40829	+	6.61672i	−0.146024	+	0.401197i
$273$	−19.3135	+	10.9627i	−1.16891	+	0.663495i
$274$	7.08281	+	4.08926i	0.427888	+	0.247041i
$275$	−24.9928	+	4.40691i	−1.50712	+	0.265747i
$276$	−7.24672	+	13.1377i	−0.436201	+	0.790797i
$277$	18.6650			1.12147			0.560737	−	0.827994i	$-0.310518\pi$
$277$	18.6650			1.12147			0.560737	+	0.827994i	$0.310518\pi$
$278$	−8.70066			−0.521831
$279$	0.885227	−	1.14279i	0.0529971	−	0.0684172i
$280$	−0.245835	−	0.453505i	−0.0146915	−	0.0271021i
$281$	−0.399945	−	2.26820i	−0.0238587	−	0.135309i	0.970552	−	0.240893i	$-0.0774402\pi$
$281$	−0.399945	−	2.26820i	−0.0238587	−	0.135309i	−0.994410	+	0.105583i	$0.966329\pi$
$282$	−1.33711	−	0.457300i	−0.0796238	−	0.0272318i
$283$	−5.14434	+	29.1750i	−0.305799	+	1.73427i	0.313921	+	0.949449i	$0.398357\pi$
$283$	−5.14434	+	29.1750i	−0.305799	+	1.73427i	−0.619720	+	0.784823i	$0.712754\pi$
$284$	6.02742	+	10.4398i	0.357662	+	0.619488i
$285$	0.853077	+	1.19962i	0.0505319	+	0.0710593i
$286$	−24.7860			−1.46563
$287$	20.8130	−	11.2823i	1.22855	−	0.665973i
$288$	2.99771	−	0.117152i	0.176642	−	0.00690327i
$289$	30.6159	+	11.1433i	1.80094	+	0.655488i
$290$	0.132162	+	0.363112i	0.00776082	+	0.0213227i
$291$	7.09820	−	0.138648i	0.416104	−	0.00812769i
$292$	−3.03981			−0.177892
$293$	−2.93758	+	5.08804i	−0.171615	+	0.297246i	−0.938985	−	0.343959i	$-0.888232\pi$
$293$	−2.93758	+	5.08804i	−0.171615	+	0.297246i	0.767369	+	0.641205i	$0.221565\pi$
$294$	−11.8612	−	2.51224i	−0.691761	−	0.146517i
$295$	−0.802260	−	0.956097i	−0.0467094	−	0.0556661i
$296$	−0.661000	+	0.381628i	−0.0384198	+	0.0221817i
$297$	14.6130	+	22.1979i	0.847929	+	1.28805i
$298$	−1.45444	+	0.256456i	−0.0842532	+	0.0148561i
$299$	32.1583	+	26.9840i	1.85976	+	1.56053i
$300$	−0.167841	−	8.59277i	−0.00969032	−	0.496104i
$301$	0.465252	−	17.3185i	0.0268167	−	0.998223i
$302$	6.57339	−	7.83386i	0.378256	−	0.450788i
$303$	4.68357	+	3.77660i	0.269064	+	0.216960i
$304$	3.97276	−	1.79365i	0.227854	−	0.102873i
$305$	1.72378	−	0.995222i	0.0987031	−	0.0569863i
$306$	−0.824912	−	21.1080i	−0.0471571	−	1.20666i
$307$	−0.890063	−	2.44543i	−0.0507986	−	0.139568i	0.911699	−	0.410860i	$-0.134771\pi$
$307$	−0.890063	−	2.44543i	−0.0507986	−	0.139568i	−0.962497	+	0.271292i	$0.912549\pi$
$308$	−10.1287	−	8.97335i	−0.577135	−	0.511304i
$309$	−22.9770	−	7.85827i	−1.30711	−	0.447041i
$310$	0.0719679	−	0.0603882i	0.00408750	−	0.00342982i
$311$	23.2489	+	13.4227i	1.31832	+	0.761134i	0.983459	−	0.181133i	$-0.0579764\pi$
$311$	23.2489	+	13.4227i	1.31832	+	0.761134i	0.334864	+	0.942267i	$0.391310\pi$
$312$	1.29586	−	8.29318i	0.0733635	−	0.469509i
$313$	−1.41297	−	8.01338i	−0.0798661	−	0.452943i	−0.998347	−	0.0574773i	$-0.981694\pi$
$313$	−1.41297	−	8.01338i	−0.0798661	−	0.452943i	0.918481	−	0.395466i	$-0.129417\pi$
$314$	11.3046	−	9.48570i	0.637957	−	0.535309i
$315$	1.19754	+	0.980206i	0.0674739	+	0.0552284i
$316$	−3.68482	+	2.12743i	−0.207287	+	0.119677i
$317$	−10.0063	+	8.39626i	−0.562009	+	0.471581i	−0.878983	−	0.476853i	$-0.841777\pi$
$317$	−10.0063	+	8.39626i	−0.562009	+	0.471581i	0.316975	+	0.948434i	$0.397333\pi$
$318$	4.28112	−	0.841398i	0.240074	−	0.0471833i
$319$	6.51562	+	7.76502i	0.364805	+	0.434757i
$320$	0.192011	+	0.0338567i	0.0107337	+	0.00189265i
$321$	−12.8802	−	14.7549i	−0.718901	−	0.823539i
$322$	3.37223	+	22.6692i	0.187927	+	1.26331i
$323$	−12.6297	−	27.9737i	−0.702736	−	1.55650i
$324$	−8.19121	+	3.72881i	−0.455067	+	0.207156i
$325$	−23.6813	−	4.17565i	−1.31360	−	0.231623i
$326$	−6.92111	−	5.80750i	−0.383325	−	0.321648i
$327$	16.7458	−	30.3588i	0.926047	−	1.67885i
$328$	−1.55381	+	8.81210i	−0.0857949	+	0.486567i
$329$	−2.04754	+	0.683552i	−0.112884	+	0.0376855i
$330$	0.622322	+	1.61119i	0.0342577	+	0.0886933i
$331$	23.9164	−	13.8081i	1.31456	−	0.758963i	0.331714	−	0.943380i	$-0.392373\pi$
$331$	23.9164	−	13.8081i	1.31456	−	0.758963i	0.982848	+	0.184418i	$0.0590399\pi$
$332$	1.97984	−	5.43955i	0.108658	−	0.298534i
$333$	1.40222	−	1.81020i	0.0768409	−	0.0991986i
$334$	2.59346	+	4.49201i	0.141908	+	0.245792i
$335$	0.131257	+	0.227343i	0.00717133	+	0.0124211i
$336$	3.53195	−	2.91982i	0.192683	−	0.159289i
$337$	−17.3056	−	3.05145i	−0.942697	−	0.166223i	−0.318882	−	0.947795i	$-0.603307\pi$
$337$	−17.3056	−	3.05145i	−0.942697	−	0.166223i	−0.623816	+	0.781572i	$0.714418\pi$
$338$	−9.85301	−	3.58620i	−0.535933	−	0.195064i
$339$	13.6981	+	15.6919i	0.743979	+	0.852268i
$340$	0.238397	−	1.35202i	0.0129289	−	0.0733235i
$341$	1.23222	−	2.13427i	0.0667285	−	0.115577i
$342$	−8.99536	+	9.49123i	−0.486413	+	0.513227i
$343$	−16.7323	+	7.93916i	−0.903459	+	0.428674i
$344$	5.01617	+	4.20907i	0.270454	+	0.226938i
$345$	0.946650	−	2.76793i	0.0509659	−	0.149021i
$346$	−9.05318	+	7.59652i	−0.486702	+	0.408391i
$347$	−7.96967	−	21.8965i	−0.427834	−	1.17546i	−0.947124	−	0.320867i	$-0.896026\pi$
$347$	−7.96967	−	21.8965i	−0.427834	−	1.17546i	0.519290	−	0.854598i	$-0.326196\pi$
$348$	−2.93875	+	1.77410i	−0.157534	+	0.0951017i
$349$	7.84067	+	13.5804i	0.419701	+	0.726944i	0.995909	−	0.0903591i	$-0.0288015\pi$
$349$	7.84067	+	13.5804i	0.419701	+	0.726944i	−0.576208	+	0.817303i	$0.695468\pi$
$350$	−8.16552	−	10.2798i	−0.436465	−	0.549476i
$351$	5.81737	+	24.5003i	0.310508	+	1.30773i
$352$	5.03686	−	0.888134i	0.268466	−	0.0473377i
$353$			2.33811i			0.124445i	0.998062	+	0.0622225i	$0.0198188\pi$
$353$			2.33811i			0.124445i	−0.998062	+	0.0622225i	$0.980181\pi$
$354$	6.95968	−	8.63109i	0.369903	−	0.458737i
$355$	−1.51079	−	1.80049i	−0.0801843	−	0.0955600i
$356$	0.163655	−	0.928132i	0.00867368	−	0.0491909i
$357$	−20.5595	−	24.8697i	−1.08813	−	1.31625i
$358$	−20.0212	+	7.28712i	−1.05815	+	0.385136i
$359$	6.83782	+	18.7868i	0.360886	+	0.991527i	0.978717	+	0.205216i	$0.0657896\pi$
$359$	6.83782	+	18.7868i	0.360886	+	0.991527i	−0.617830	+	0.786311i	$0.711988\pi$
$360$	−0.571627	+	0.123987i	−0.0301274	+	0.00653470i
$361$	−6.93359	+	17.6897i	−0.364926	+	0.931037i
$362$	−8.93173	−	5.15674i	−0.469441	−	0.271032i
$363$	17.2664	+	19.7796i	0.906252	+	1.03816i
$364$	−6.11037	−	11.2721i	−0.320271	−	0.590820i
$365$	0.583678	−	0.102918i	0.0305511	−	0.00538698i
$366$	11.6283	+	13.3208i	0.607819	+	0.696289i
$367$	−4.18884	−	23.7561i	−0.218656	−	1.24006i	−0.874449	−	0.485117i	$-0.838777\pi$
$367$	−4.18884	−	23.7561i	−0.218656	−	1.24006i	0.655793	−	0.754940i	$-0.272334\pi$
$368$	−7.50190	−	4.33123i	−0.391064	−	0.225781i
$369$	−5.69024	−	26.2341i	−0.296222	−	1.36569i
$370$	0.113999	−	0.0956561i	0.00592650	−	0.00497292i
$371$	4.41950	−	4.98852i	0.229449	−	0.258991i
$372$	0.649684	+	0.523874i	0.0336846	+	0.0271616i
$373$			9.96766i			0.516106i	0.966131	+	0.258053i	$0.0830809\pi$
$373$			9.96766i			0.516106i	−0.966131	+	0.258053i	$0.916919\pi$
$374$	−6.25368	−	35.4664i	−0.323370	−	1.83392i
$375$	0.648776	+	3.30104i	0.0335027	+	0.170465i
$376$	0.279048	−	0.766678i	0.0143908	−	0.0395384i
$377$	3.28496	+	9.02536i	0.169184	+	0.464830i
$378$	−6.49266	+	12.1180i	−0.333946	+	0.623282i
$379$		−	37.5428i		−	1.92844i	−0.265098	−	0.964222i	$-0.585404\pi$
$379$		−	37.5428i		−	1.92844i	0.265098	−	0.964222i	$-0.414596\pi$
$380$	−0.702087	+	0.478904i	−0.0360163	+	0.0245673i
$381$	−9.30597	+	3.59442i	−0.476760	+	0.184148i
$382$	16.0262	+	2.82586i	0.819973	+	0.144583i
$383$	−4.09110	+	23.2018i	−0.209045	+	1.18556i	0.681900	+	0.731445i	$0.261154\pi$
$383$	−4.09110	+	23.2018i	−0.209045	+	1.18556i	−0.890946	+	0.454110i	$0.849957\pi$
$384$	0.0338254	+	1.73172i	0.00172615	+	0.0883715i
$385$	2.24863	+	1.38006i	0.114601	+	0.0703343i
$386$	−0.432393	+	1.18799i	−0.0220082	+	0.0604671i
$387$	−18.7080	−	5.99280i	−0.950983	−	0.304631i
$388$			4.09893i			0.208092i
$389$	4.42826	−	12.1665i	0.224522	−	0.616868i	−0.775371	−	0.631506i	$-0.782437\pi$
$389$	4.42826	−	12.1665i	0.224522	−	0.616868i	0.999893	+	0.0146376i	$0.00465947\pi$
$390$	0.0319607	+	1.63625i	0.00161839	+	0.0828550i
$391$	−30.4977	+	52.8236i	−1.54234	+	2.67141i
$392$	1.58391	−	6.81845i	0.0799993	−	0.344384i
$393$	−5.40354	+	9.79618i	−0.272573	+	0.494152i
$394$	12.5710	−	14.9815i	0.633316	−	0.754756i
$395$	0.635497	−	0.533246i	0.0319753	−	0.0268305i
$396$	−12.9783	+	8.18490i	−0.652184	+	0.411307i
$397$	11.4719	−	4.17543i	0.575758	−	0.209559i	−0.0376962	−	0.999289i	$-0.512002\pi$
$397$	11.4719	−	4.17543i	0.575758	−	0.209559i	0.613454	+	0.789731i	$0.289780\pi$
$398$	8.99283			0.450770
$399$	−2.13002	+	19.8611i	−0.106635	+	0.994298i
$400$	4.96199			0.248099
$401$	−17.5502	+	6.38776i	−0.876417	+	0.318990i	−0.740763	−	0.671767i	$-0.765536\pi$
$401$	−17.5502	+	6.38776i	−0.876417	+	0.318990i	−0.135654	+	0.990756i	$0.543314\pi$
$402$	−1.75684	+	1.53362i	−0.0876232	+	0.0764898i
$403$	1.78880	−	1.50099i	0.0891067	−	0.0747694i
$404$	−2.23281	+	2.66096i	−0.111087	+	0.132388i
$405$	1.44656	−	0.993300i	0.0718800	−	0.0493575i
$406$	−1.92509	+	4.87743i	−0.0955407	+	0.242063i
$407$	1.95186	−	3.38072i	0.0967502	−	0.167576i
$408$	12.1937	−	0.238177i	0.603677	−	0.0117915i
$409$	−8.58481	+	23.5866i	−0.424491	+	1.16628i	0.524619	+	0.851337i	$0.324208\pi$
$409$	−8.58481	+	23.5866i	−0.424491	+	1.16628i	−0.949110	+	0.314943i	$0.898014\pi$
$410$		−	1.74463i		−	0.0861610i
$411$	2.18693	−	13.9958i	0.107873	−	0.690361i
$412$	4.79517	−	13.1746i	0.236241	−	0.649068i
$413$	0.454824	−	16.9303i	0.0223804	−	0.833087i
$414$	25.7493	+	3.50981i	1.26551	+	0.172498i
$415$	−0.195985	+	1.11148i	−0.00962051	+	0.0545606i
$416$	4.77254	+	0.841528i	0.233993	+	0.0412593i
$417$	5.42981	+	14.0578i	0.265899	+	0.688413i
$418$	−13.0099	+	18.1041i	−0.636333	+	0.885502i
$419$		−	5.69757i		−	0.278345i	−0.990268	−	0.139172i	$-0.955556\pi$
$419$		−	5.69757i		−	0.278345i	0.990268	−	0.139172i	$-0.0444442\pi$
$420$	−0.579317	+	0.680218i	−0.0282678	+	0.0331912i
$421$	0.419139	+	1.15157i	0.0204276	+	0.0561243i	0.949487	−	0.313805i	$-0.101604\pi$
$421$	0.419139	+	1.15157i	0.0204276	+	0.0561243i	−0.929060	+	0.369930i	$0.879382\pi$
$422$	6.53518	−	17.9553i	0.318128	−	0.874049i
$423$	0.0955825	+	2.44578i	0.00464738	+	0.118918i
$424$	0.437419	+	2.48072i	0.0212429	+	0.120475i
$425$		−	34.9391i		−	1.69480i
$426$	13.1062	−	16.2538i	0.634999	−	0.787497i
$427$	26.4641	+	5.40287i	1.28069	+	0.261463i
$428$	8.66236	−	7.26858i	0.418711	−	0.351340i
$429$	15.4682	+	40.0472i	0.746811	+	1.93350i
$430$	−1.10567	−	0.638356i	−0.0533199	−	0.0307843i
$431$	−2.19873	−	12.4696i	−0.105909	−	0.600641i	−0.990853	−	0.134944i	$-0.956915\pi$
$431$	−2.19873	−	12.4696i	−0.105909	−	0.600641i	0.884944	−	0.465697i	$-0.154196\pi$
$432$	−2.06006	−	4.77034i	−0.0991148	−	0.229513i
$433$	16.0890	−	2.83692i	0.773186	−	0.136333i	0.226884	−	0.973922i	$-0.427146\pi$
$433$	16.0890	−	2.83692i	0.773186	−	0.136333i	0.546302	+	0.837588i	$0.316035\pi$
$434$	1.27439	+	0.0342358i	0.0611727	+	0.00164337i
$435$	0.504208	−	0.440143i	0.0241749	−	0.0211032i
$436$	17.3355	+	10.0087i	0.830221	+	0.479329i
$437$	36.5891	−	9.32541i	1.75029	−	0.446095i
$438$	1.89705	+	4.91148i	0.0906447	+	0.234679i
$439$	−2.91902	−	8.01994i	−0.139317	−	0.382771i	0.850338	−	0.526237i	$-0.176397\pi$
$439$	−2.91902	−	8.01994i	−0.139317	−	0.382771i	−0.989655	+	0.143466i	$0.954175\pi$
$440$	−0.937063	+	0.341063i	−0.0446727	+	0.0162595i
$441$	3.34315	+	20.7322i	0.159197	+	0.987247i
$442$	5.92551	−	33.6052i	0.281848	−	1.59844i
$443$	1.92385	+	2.29276i	0.0914050	+	0.108932i	0.809808	−	0.586695i	$-0.199571\pi$
$443$	1.92385	+	2.29276i	0.0914050	+	0.108932i	−0.718403	+	0.695627i	$0.755127\pi$
$444$	1.02911	+	0.829825i	0.0488395	+	0.0393818i
$445$			0.183752i			0.00871070i
$446$	−18.7661	+	3.30896i	−0.888599	+	0.156684i
$447$	1.32203	+	2.18991i	0.0625298	+	0.103579i
$448$	1.64561	+	2.07170i	0.0777480	+	0.0978788i
$449$	6.74168	+	11.6769i	0.318160	+	0.551069i	0.980104	−	0.198484i	$-0.0636019\pi$
$449$	6.74168	+	11.6769i	0.318160	+	0.551069i	−0.661944	+	0.749553i	$0.730269\pi$
$450$	−13.7787	+	5.63366i	−0.649536	+	0.265573i
$451$	−15.6527	−	43.0053i	−0.737055	−	2.02504i
$452$	−9.21245	+	7.73017i	−0.433317	+	0.363596i
$453$	−16.7595	−	5.73186i	−0.787432	−	0.269307i
$454$	13.4739	+	11.3060i	0.632363	+	0.530616i
$455$	1.55490	+	1.95749i	0.0728946	+	0.0917688i
$456$	−5.37730	−	5.29950i	−0.251815	−	0.248172i
$457$	−12.1969	+	21.1256i	−0.570546	+	0.988215i	0.425963	+	0.904740i	$0.359935\pi$
$457$	−12.1969	+	21.1256i	−0.570546	+	0.988215i	−0.996510	+	0.0834751i	$0.973398\pi$
$458$	0.779858	−	4.42279i	0.0364404	−	0.206664i
$459$	−33.5897	+	14.5057i	−1.56783	+	0.677066i
$460$	1.58709	+	0.577653i	0.0739984	+	0.0269332i
$461$	−25.9455	−	4.57490i	−1.20840	−	0.213074i	−0.467076	−	0.884217i	$-0.654692\pi$
$461$	−25.9455	−	4.57490i	−1.20840	−	0.213074i	−0.741328	+	0.671143i	$0.765804\pi$
$462$	−8.17739	+	21.9651i	−0.380447	+	1.02191i
$463$	15.2156	+	26.3542i	0.707128	+	1.22478i	0.965918	+	0.258848i	$0.0833428\pi$
$463$	15.2156	+	26.3542i	0.707128	+	1.22478i	−0.258790	+	0.965934i	$0.583324\pi$
$464$	−0.990946	−	1.71637i	−0.0460035	−	0.0796804i
$465$	−0.142483	−	0.0785933i	−0.00660750	−	0.00364468i
$466$	−3.50328	+	9.62517i	−0.162286	+	0.445878i
$467$	21.3685	−	12.3371i	0.988816	−	0.570893i	0.0838961	−	0.996475i	$-0.473264\pi$
$467$	21.3685	−	12.3371i	0.988816	−	0.570893i	0.904920	+	0.425581i	$0.139930\pi$
$468$	−14.2081	+	3.08177i	−0.656771	+	0.142455i
$469$	−0.712568	+	3.49027i	−0.0329033	+	0.161166i
$470$	−0.0276231	+	0.156658i	−0.00127416	+	0.00722611i
$471$	−22.3811	−	12.3453i	−1.03127	−	0.568843i
$472$	4.90374	+	4.11472i	0.225713	+	0.189396i
$473$	−32.9821	−	5.81563i	−1.51652	−	0.267403i
$474$	5.73690	+	4.62595i	0.263505	+	0.212477i
$475$	−15.4800	+	15.1055i	−0.710270	+	0.693087i
$476$	14.5876	−	11.5874i	0.668622	−	0.531106i
$477$	−4.03118	−	6.39199i	−0.184575	−	0.292669i
$478$	−21.2815	−	3.75250i	−0.973394	−	0.171636i
$479$	12.1365	+	14.4637i	0.554530	+	0.660863i	0.968379	−	0.249482i	$-0.0802604\pi$
$479$	12.1365	+	14.4637i	0.554530	+	0.660863i	−0.413849	+	0.910345i	$0.635816\pi$
$480$	−0.0651252	−	0.331364i	−0.00297255	−	0.0151246i
$481$	2.83350	−	2.37759i	0.129196	−	0.108409i
$482$	−0.179358	+	0.103552i	−0.00816953	+	0.00471668i
$483$	34.5226	−	19.5957i	1.57083	−	0.891637i
$484$	−11.6123	+	9.74385i	−0.527830	+	0.442902i
$485$	−0.138776	−	0.787040i	−0.00630151	−	0.0357376i
$486$	11.1366	+	10.9076i	0.505166	+	0.494780i
$487$	21.3002	+	12.2977i	0.965203	+	0.557260i	0.897771	−	0.440463i	$-0.145186\pi$
$487$	21.3002	+	12.2977i	0.965203	+	0.557260i	0.0674327	+	0.997724i	$0.478519\pi$
$488$	−7.82041	+	6.56210i	−0.354013	+	0.297052i
$489$	−5.06402	+	14.8068i	−0.229003	+	0.669588i
$490$	−0.0732769	+	1.36284i	−0.00331031	+	0.0615670i
$491$	2.34057	+	6.43066i	0.105628	+	0.290212i	0.981236	−	0.192812i	$-0.0617607\pi$
$491$	2.34057	+	6.43066i	0.105628	+	0.290212i	−0.875607	+	0.483024i	$0.839539\pi$
$492$	15.2075	−	2.98884i	0.685609	−	0.134747i
$493$	−12.0856	+	6.97761i	−0.544307	+	0.314256i
$494$	−17.4508	+	11.9034i	−0.785148	+	0.535561i
$495$	2.21486	−	2.01099i	0.0995506	−	0.0903874i
$496$	−0.309726	+	0.369117i	−0.0139071	+	0.0165739i
$497$	0.856509	−	31.8826i	0.0384197	−	1.43013i
$498$	−10.0243	+	0.195804i	−0.449201	+	0.00877417i
$499$	−20.9699	−	17.5959i	−0.938743	−	0.787699i	0.0386229	−	0.999254i	$-0.487703\pi$
$499$	−20.9699	−	17.5959i	−0.938743	−	0.787699i	−0.977366	+	0.211555i	$0.932147\pi$
$500$	−1.91281	+	0.337280i	−0.0855435	+	0.0150836i
$501$	5.63931	−	6.99363i	0.251946	−	0.312452i
$502$	23.1091	−	13.3421i	1.03141	−	0.595486i
$503$	3.32057	+	3.95730i	0.148057	+	0.176447i	0.834976	−	0.550287i	$-0.185482\pi$
$503$	3.32057	+	3.95730i	0.148057	+	0.176447i	−0.686919	+	0.726734i	$0.741037\pi$
$504$	−6.92178	−	3.88445i	−0.308321	−	0.173027i
$505$	0.338633	−	0.586530i	0.0150690	−	0.0261002i
$506$	44.3046			1.96958
$507$	0.354671	+	18.1577i	0.0157515	+	0.806412i
$508$	−1.96992	−	5.41231i	−0.0874011	−	0.240132i
$509$	24.1465	+	8.78861i	1.07028	+	0.389548i	0.816280	−	0.577657i	$-0.196033\pi$
$509$	24.1465	+	8.78861i	1.07028	+	0.389548i	0.253996	+	0.967205i	$0.418255\pi$
$510$	−2.33326	+	0.458570i	−0.103318	+	0.0203058i
$511$	6.85459	+	4.20689i	0.303229	+	0.186102i
$512$	−1.00000			−0.0441942
$513$	20.9489	+	8.61076i	0.924915	+	0.380174i
$514$	0.832108	+	1.44125i	0.0367027	+	0.0635710i
$515$	−0.474676	+	2.69202i	−0.0209167	+	0.118625i
$516$	3.67022	−	10.7315i	0.161573	−	0.472426i
$517$	0.724613	+	4.10948i	0.0318684	+	0.180735i
$518$	2.01866	+	0.0542301i	0.0886948	+	0.00238274i
$519$	17.9236	+	9.88661i	0.786760	+	0.433974i
$520$	−0.944872			−0.0414354
$521$	29.3970			1.28791			0.643953	−	0.765065i	$-0.277293\pi$
$521$	29.3970			1.28791			0.643953	+	0.765065i	$0.277293\pi$
$522$	4.70042	+	3.64103i	0.205732	+	0.159364i
$523$	−33.3222	+	5.87561i	−1.45708	+	0.256922i	−0.845379	−	0.534168i	$-0.820625\pi$
$523$	−33.3222	+	5.87561i	−1.45708	+	0.256922i	−0.611700	+	0.791090i	$0.709514\pi$
$524$	−5.59382	−	3.22959i	−0.244367	−	0.141085i
$525$	−11.5133	+	19.6084i	−0.502483	+	0.855782i
$526$	−3.37069	+	9.26089i	−0.146969	+	0.403794i
$527$	2.59909	+	2.18089i	0.113218	+	0.0950013i
$528$	−4.57832	−	7.58388i	−0.199246	−	0.330046i
$529$	−39.8635	−	33.4494i	−1.73319	−	1.45432i
$530$	−0.167978	−	0.461517i	−0.00729651	−	0.0200470i
$531$	−18.2887	−	5.85848i	−0.793662	−	0.254236i
$532$	−11.4406	−	1.45347i	−0.496013	−	0.0630160i
$533$		−	43.3637i		−	1.87829i
$534$	−1.60173	+	0.314799i	−0.0693136	+	0.0136227i
$535$	−1.41718	+	1.68893i	−0.0612699	+	0.0730187i
$536$	−0.865456	−	1.03141i	−0.0373820	−	0.0445501i
$537$	24.2685	+	27.8009i	1.04726	+	1.19970i
$538$	6.61666	+	2.40827i	0.285265	+	0.103828i
$539$	10.4210	+	34.2517i	0.448866	+	1.47533i
$540$	0.557063	+	0.846211i	0.0239722	+	0.0364151i
$541$	7.45137	+	42.2588i	0.320359	+	1.81685i	0.540458	+	0.841371i	$0.318251\pi$
$541$	7.45137	+	42.2588i	0.320359	+	1.81685i	−0.220099	+	0.975478i	$0.570638\pi$
$542$	26.1634	+	9.52269i	1.12381	+	0.409035i
$543$	−2.75781	+	17.6493i	−0.118349	+	0.757404i
$544$			7.04136i			0.301896i
$545$	−3.66747	−	1.33485i	−0.157097	−	0.0571787i
$546$	−14.3993	+	16.9072i	−0.616231	+	0.723562i
$547$	−23.9409	+	4.22143i	−1.02364	+	0.180496i	−0.660175	−	0.751112i	$-0.729518\pi$
$547$	−23.9409	+	4.22143i	−1.02364	+	0.180496i	−0.363466	+	0.931607i	$0.618407\pi$
$548$	8.05427	+	1.42019i	0.344061	+	0.0606673i
$549$	14.2658	−	27.1010i	0.608849	−	1.15664i
$550$	−21.9783	+	12.6892i	−0.937159	+	0.541069i
$551$	8.31651	+	2.33790i	0.354295	+	0.0995979i
$552$	−2.31633	+	14.8239i	−0.0985894	+	0.630948i
$553$	11.2532	+	0.302312i	0.478536	+	0.0128556i
$554$	17.5394	−	6.38382i	0.745178	−	0.271222i
$555$	−0.225696	−	0.124493i	−0.00958026	−	0.00528444i
$556$	−8.17595	+	2.97580i	−0.346737	+	0.126202i
$557$	37.7627	−	6.65859i	1.60006	−	0.282134i	0.698768	−	0.715348i	$-0.253732\pi$
$557$	37.7627	−	6.65859i	1.60006	−	0.282134i	0.901291	+	0.433215i	$0.142621\pi$
$558$	0.440983	−	1.37664i	0.0186683	−	0.0582778i
$559$	−27.4819	−	15.8667i	−1.16236	−	0.671090i
$560$	−0.386117	−	0.342075i	−0.0163164	−	0.0144553i
$561$	−53.4008	+	32.2376i	−2.25459	+	1.36107i
$562$	−1.15160	−	1.99462i	−0.0485771	−	0.0841380i
$563$	−17.2869	+	29.9418i	−0.728555	+	1.26189i	0.228939	+	0.973441i	$0.426475\pi$
$563$	−17.2869	+	29.9418i	−0.728555	+	1.26189i	−0.957494	+	0.288454i	$0.906859\pi$
$564$	−1.41288	+	0.0275976i	−0.0594930	+	0.00116207i
$565$	1.50717	−	1.79618i	0.0634073	−	0.0755659i
$566$	5.14434	+	29.1750i	0.216233	+	1.22632i
$567$	23.6311	+	2.92784i	0.992412	+	0.122958i
$568$	9.23455	+	7.74871i	0.387473	+	0.325128i
$569$	5.85842	−	10.1471i	0.245598	−	0.425388i	−0.716702	−	0.697380i	$-0.754349\pi$
$569$	5.85842	−	10.1471i	0.245598	−	0.425388i	0.962299	+	0.271992i	$0.0876825\pi$
$570$	1.21192	+	0.835504i	0.0507619	+	0.0349954i
$571$	−6.21536	−	10.7653i	−0.260105	−	0.450514i	0.706165	−	0.708047i	$-0.250424\pi$
$571$	−6.21536	−	10.7653i	−0.260105	−	0.450514i	−0.966269	+	0.257533i	$0.917090\pi$
$572$	−23.2912	+	8.47732i	−0.973856	+	0.354455i
$573$	−5.43569	−	27.6574i	−0.227079	−	1.15540i
$574$	15.6991	−	17.7204i	0.655267	−	0.739634i
$575$	42.3300	+	7.46391i	1.76528	+	0.311267i
$576$	2.77686	−	1.13536i	0.115702	−	0.0473069i
$577$	11.0774	−	19.1867i	0.461160	−	0.798752i	−0.537859	−	0.843035i	$-0.680767\pi$
$577$	11.0774	−	19.1867i	0.461160	−	0.798752i	0.999019	+	0.0442824i	$0.0141001\pi$
$578$	32.5808			1.35518
$579$	2.18930	−	0.0427632i	0.0909841	−	0.00177718i
$580$	0.248383	+	0.296012i	0.0103135	+	0.0122912i
$581$	−11.9924	+	9.52589i	−0.497527	+	0.395201i
$582$	6.62271	−	2.55801i	0.274520	−	0.106033i
$583$	−8.28138	−	9.86937i	−0.342980	−	0.408747i
$584$	−2.85649	+	1.03968i	−0.118202	+	0.0430222i
$585$	2.62378	−	1.07277i	0.108480	−	0.0443538i
$586$	−1.02021	+	5.78590i	−0.0421445	+	0.239013i
$587$	−10.8724	+	12.9572i	−0.448752	+	0.534802i	−0.942235	−	0.334954i	$-0.891279\pi$
$587$	−10.8724	+	12.9572i	−0.448752	+	0.534802i	0.493482	+	0.869756i	$0.335724\pi$
$588$	−12.0051	+	1.69604i	−0.495084	+	0.0699435i
$589$	−0.157425	−	2.09442i	−0.00648658	−	0.0862991i
$590$	−1.08088	−	0.624048i	−0.0444992	−	0.0256916i
$591$	−32.0510	−	10.9616i	−1.31840	−	0.450901i
$592$	−0.490612	+	0.584689i	−0.0201640	+	0.0240306i
$593$	−1.68350	+	4.62539i	−0.0691333	+	0.189942i	−0.969448	−	0.245298i	$-0.921114\pi$
$593$	−1.68350	+	4.62539i	−0.0691333	+	0.189942i	0.900314	+	0.435240i	$0.143336\pi$
$594$	21.3238	+	15.8613i	0.874927	+	0.650797i
$595$	−2.40867	+	2.71879i	−0.0987459	+	0.111460i
$596$	−1.27901	+	0.738436i	−0.0523902	+	0.0302475i
$597$	−5.61215	−	14.5299i	−0.229690	−	0.594668i
$598$	39.4480	+	14.3579i	1.61315	+	0.587138i
$599$	−21.0988	−	7.67933i	−0.862073	−	0.313769i	−0.127121	−	0.991887i	$-0.540574\pi$
$599$	−21.0988	−	7.67933i	−0.862073	−	0.313769i	−0.734953	+	0.678118i	$0.762796\pi$
$600$	−3.09662	−	8.01716i	−0.126419	−	0.327299i
$601$	37.3662	−	21.5734i	1.52420	−	0.879996i	0.524608	−	0.851344i	$-0.324212\pi$
$601$	37.3662	−	21.5734i	1.52420	−	0.879996i	0.999589	−	0.0286522i	$-0.00912152\pi$
$602$	−5.48609	−	16.4332i	−0.223596	−	0.669768i
$603$	3.57427	+	1.88147i	0.145556	+	0.0766195i
$604$	3.49763	−	9.60966i	0.142317	−	0.391011i
$605$	1.89979	−	2.26408i	0.0772374	−	0.0920479i
$606$	5.69279	+	1.94697i	0.231254	+	0.0790901i
$607$	6.31932	+	3.64846i	0.256493	+	0.148086i	0.622734	−	0.782434i	$-0.286022\pi$
$607$	6.31932	+	3.64846i	0.256493	+	0.148086i	−0.366241	+	0.930520i	$0.619355\pi$
$608$	3.11971	−	3.04424i	0.126521	−	0.123460i
$609$	9.08193	+	0.0665501i	0.368018	+	0.00269675i
$610$	1.27943	−	1.52477i	0.0518027	−	0.0617361i
$611$	−0.686588	+	3.89383i	−0.0277764	+	0.157528i
$612$	−7.99452	−	19.5529i	−0.323159	−	0.790378i
$613$	24.4299	−	8.89176i	0.986715	−	0.359135i	0.202267	−	0.979330i	$-0.435169\pi$
$613$	24.4299	−	8.89176i	0.986715	−	0.359135i	0.784447	+	0.620196i	$0.212947\pi$
$614$	−1.67277	−	1.99353i	−0.0675075	−	0.0804523i
$615$	−2.81882	+	1.08877i	−0.113666	+	0.0439033i
$616$	−12.5869	−	4.96798i	−0.507141	−	0.200166i
$617$	−14.7794	−	17.6134i	−0.594997	−	0.709090i	0.381561	−	0.924344i	$-0.375387\pi$
$617$	−14.7794	−	17.6134i	−0.594997	−	0.709090i	−0.976558	+	0.215254i	$0.930942\pi$
$618$	−24.2790	+	0.474238i	−0.976644	+	0.0190766i
$619$	39.3030			1.57972			0.789860	−	0.613287i	$-0.210153\pi$
$619$	39.3030			1.57972			0.789860	+	0.613287i	$0.210153\pi$
$620$	0.0469737	−	0.0813609i	0.00188651	−	0.00326753i
$621$	−10.3985	−	43.7938i	−0.417276	−	1.75739i
$622$	26.4376	+	4.66167i	1.06005	+	0.186916i
$623$	−1.65350	+	1.86639i	−0.0662461	+	0.0747754i
$624$	−1.61873	−	8.23625i	−0.0648009	−	0.329714i
$625$	−22.9578	+	8.35597i	−0.918314	+	0.334239i
$626$	−4.06850	−	7.04685i	−0.162610	−	0.281649i
$627$	37.3702	+	9.72201i	1.49242	+	0.388260i
$628$	7.37857	−	12.7801i	0.294437	−	0.509980i
$629$	4.11701	+	3.45458i	0.164156	+	0.137743i
$630$	1.46057	+	0.511509i	0.0581906	+	0.0203790i
$631$	6.58941	+	37.3704i	0.262320	+	1.48769i	0.776559	+	0.630045i	$0.216964\pi$
$631$	6.58941	+	37.3704i	0.262320	+	1.48769i	−0.514238	+	0.857647i	$0.671925\pi$
$632$	−2.73497	+	3.25941i	−0.108791	+	0.129652i
$633$	−33.0890	+	0.646323i	−1.31517	+	0.0256890i
$634$	−6.53113	+	11.3123i	−0.259384	+	0.449267i
$635$	0.561489	+	0.972528i	0.0222820	+	0.0385936i
$636$	3.73517	−	2.25489i	0.148109	−	0.0894121i
$637$	−1.82134	+	33.8743i	−0.0721641	+	1.34215i
$638$	8.77848	+	5.06825i	0.347543	+	0.200654i
$639$	−34.4406	−	11.0325i	−1.36245	−	0.436438i
$640$	0.192011	−	0.0338567i	0.00758990	−	0.00133830i
$641$	−37.4058	+	13.6146i	−1.47744	+	0.537745i	−0.950110	−	0.311915i	$-0.899030\pi$
$641$	−37.4058	+	13.6146i	−1.47744	+	0.537745i	−0.527331	+	0.849660i	$0.676807\pi$
$642$	−17.1499	−	9.45982i	−0.676852	−	0.373349i
$643$	27.9950	−	10.1893i	1.10401	−	0.401828i	0.275219	−	0.961382i	$-0.411250\pi$
$643$	27.9950	−	10.1893i	1.10401	−	0.401828i	0.828794	+	0.559554i	$0.189027\pi$
$644$	10.9222	+	20.1488i	0.430395	+	0.793972i
$645$	−0.341391	+	2.18482i	−0.0134423	+	0.0860272i
$646$	−21.4356	−	21.9670i	−0.843372	−	0.864281i
$647$	−22.3907	+	12.9273i	−0.880269	+	0.508224i	−0.870747	−	0.491731i	$-0.836364\pi$
$647$	−22.3907	+	12.9273i	−0.880269	+	0.508224i	−0.00952191	+	0.999955i	$0.503031\pi$
$648$	−6.42189	+	6.30550i	−0.252276	+	0.247703i
$649$	−32.2428	−	5.68528i	−1.26564	−	0.223167i
$650$	−23.6813	+	4.17565i	−0.928857	+	0.163783i
$651$	−0.739992	−	2.08042i	−0.0290026	−	0.0815381i
$652$	−8.49000	−	3.09011i	−0.332494	−	0.121018i
$653$			3.80254i			0.148805i	0.997228	+	0.0744024i	$0.0237049\pi$
$653$			3.80254i			0.148805i	−0.997228	+	0.0744024i	$0.976295\pi$
$654$	5.35261	−	34.2554i	0.209304	−	1.33949i
$655$	1.18342	+	0.430729i	0.0462400	+	0.0168300i
$656$	1.55381	+	8.81210i	0.0606662	+	0.344055i
$657$	6.75166	−	6.13020i	0.263407	−	0.239162i
$658$	−1.69027	+	1.34263i	−0.0658934	+	0.0523411i
$659$	3.76099	+	1.36889i	0.146508	+	0.0533244i	0.414233	−	0.910171i	$-0.364050\pi$
$659$	3.76099	+	1.36889i	0.146508	+	0.0533244i	−0.267726	+	0.963495i	$0.586272\pi$
$660$	1.13585	+	1.30118i	0.0442130	+	0.0506484i
$661$	−10.9009	−	12.9912i	−0.423996	−	0.505299i	0.511184	−	0.859471i	$-0.329207\pi$
$661$	−10.9009	−	12.9912i	−0.423996	−	0.505299i	−0.935180	+	0.354172i	$0.884763\pi$
$662$	17.7514	−	21.1553i	0.689926	−	0.822222i
$663$	−57.9944	+	11.3980i	−2.25232	+	0.442663i
$664$		−	5.78865i		−	0.224643i
$665$	2.24593	−	0.108259i	0.0870935	−	0.00419810i
$666$	0.698525	−	2.18062i	0.0270673	−	0.0844974i
$667$	−5.87182	−	16.1327i	−0.227358	−	0.624660i
$668$	3.97342	+	3.33409i	0.153736	+	0.129000i
$669$	17.0577	+	28.2556i	0.659487	+	1.09243i
$670$	0.201097	+	0.168741i	0.00776906	+	0.00651901i
$671$	17.8581	−	49.0648i	0.689405	−	1.89412i
$672$	2.32031	−	3.95173i	0.0895078	−	0.152441i
$673$	10.7054	+	6.18077i	0.412663	+	0.238251i	0.691933	−	0.721961i	$-0.256759\pi$
$673$	10.7054	+	6.18077i	0.412663	+	0.238251i	−0.279270	+	0.960213i	$0.590093\pi$
$674$	−17.3056	+	3.05145i	−0.666588	+	0.117537i
$675$	17.7013	+	18.7467i	0.681323	+	0.721562i
$676$	−10.4853			−0.403283
$677$	2.34131			0.0899838			0.0449919	−	0.998987i	$-0.485674\pi$
$677$	2.34131			0.0899838			0.0449919	+	0.998987i	$0.485674\pi$
$678$	18.2390	+	10.0606i	0.700463	+	0.386373i
$679$	5.67263	−	9.24282i	0.217696	−	0.354707i
$680$	−0.238397	−	1.35202i	−0.00914213	−	0.0518476i
$681$	9.85858	−	28.8258i	0.377782	−	1.10461i
$682$	0.427946	−	2.42700i	0.0163869	−	0.0929347i
$683$	−18.4048	−	31.8780i	−0.704239	−	1.21978i	−0.966965	−	0.254908i	$-0.917955\pi$
$683$	−18.4048	−	31.8780i	−0.704239	−	1.21978i	0.262726	−	0.964870i	$-0.415378\pi$
$684$	−5.20668	+	11.9954i	−0.199082	+	0.458657i
$685$	−1.59459			−0.0609262
$686$	−13.0079	+	13.1832i	−0.496643	+	0.503335i
$687$	−7.63266	+	1.50010i	−0.291204	+	0.0572323i
$688$	6.15325	+	2.23960i	0.234590	+	0.0853839i
$689$	−4.17520	−	11.4713i	−0.159062	−	0.437020i
$690$	−0.0571293	−	2.92478i	−0.00217487	−	0.111344i
$691$	−14.6152			−0.555987			−0.277993	−	0.960583i	$-0.589669\pi$
$691$	−14.6152			−0.555987			−0.277993	+	0.960583i	$0.589669\pi$
$692$	−5.90904	+	10.2348i	−0.224628	+	0.389067i
$693$	40.5925	−	0.495365i	1.54198	−	0.0188174i
$694$	−14.9781	−	17.8502i	−0.568560	−	0.677583i
$695$	1.46912	−	0.848197i	0.0557269	−	0.0321739i
$696$	−2.15475	+	2.67222i	−0.0816755	+	0.101290i
$697$	62.0492	−	10.9410i	2.35028	−	0.414418i
$698$	12.0126	+	10.0798i	0.454684	+	0.381525i
$699$	17.7378	−	0.346470i	0.670907	−	0.0131047i
$700$	−11.1890	−	6.86704i	−0.422903	−	0.259550i
$701$	−4.32171	+	5.15042i	−0.163229	+	0.194529i	−0.841459	−	0.540321i	$-0.818303\pi$
$701$	−4.32171	+	5.15042i	−0.163229	+	0.194529i	0.678230	+	0.734850i	$0.262747\pi$
$702$	13.8461	+	21.0331i	0.522588	+	0.793842i
$703$	−0.249364	−	3.31760i	−0.00940494	−	0.125126i
$704$	4.42934	−	2.55728i	0.166937	−	0.0963811i
$705$	0.270354	−	0.0531345i	0.0101821	−	0.00200116i
$706$	0.799680	+	2.19710i	0.0300964	+	0.0826891i
$707$	8.71744	−	2.91024i	0.327853	−	0.109451i
$708$	3.58796	−	10.4909i	0.134844	−	0.394273i
$709$	−16.0972	+	13.5072i	−0.604544	+	0.507272i	−0.892902	−	0.450250i	$-0.851335\pi$
$709$	−16.0972	+	13.5072i	−0.604544	+	0.507272i	0.288359	+	0.957522i	$0.406890\pi$
$710$	−2.03548	−	1.17519i	−0.0763902	−	0.0441039i
$711$	3.89401	−	12.1561i	0.146037	−	0.455890i
$712$	−0.163655	−	0.928132i	−0.00613322	−	0.0347832i
$713$	−3.19746	+	2.68299i	−0.119746	+	0.100479i
$714$	−27.8256	−	16.3381i	−1.04135	−	0.611439i
$715$	4.18516	−	2.41630i	0.156516	−	0.0903646i
$716$	−16.3214	+	13.6953i	−0.609960	+	0.511818i
$717$	7.21815	+	36.7267i	0.269567	+	1.37158i
$718$	12.8509	+	15.3151i	0.479591	+	0.571555i
$719$	−3.49931	−	0.617022i	−0.130502	−	0.0230110i	0.108016	−	0.994149i	$-0.465550\pi$
$719$	−3.49931	−	0.617022i	−0.130502	−	0.0230110i	−0.238518	+	0.971138i	$0.576661\pi$
$720$	−0.494748	+	0.312018i	−0.0184382	+	0.0116282i
$721$	−29.0456	+	23.0718i	−1.08171	+	0.859238i
$722$	−0.465209	+	18.9943i	−0.0173133	+	0.706895i
$723$	0.279243	+	0.225168i	0.0103852	+	0.00837408i
$724$	−10.1568	−	1.79092i	−0.377474	−	0.0665589i
$725$	7.53337	+	6.32125i	0.279782	+	0.234765i
$726$	22.9901	+	12.6813i	0.853244	+	0.470647i
$727$	1.77798	−	10.0835i	0.0659418	−	0.373974i	−0.933922	−	0.357477i	$-0.883637\pi$
$727$	1.77798	−	10.0835i	0.0659418	−	0.373974i	0.999864	−	0.0164979i	$-0.00525169\pi$
$728$	−9.59717	−	8.50246i	−0.355695	−	0.315122i
$729$	10.6737	−	24.8007i	0.395320	−	0.918543i
$730$	0.513278	−	0.296341i	0.0189973	−	0.0109681i
$731$	15.7698	−	43.3272i	0.583268	−	1.60252i
$732$	15.4830	+	8.54036i	0.572267	+	0.315661i
$733$	−3.82488	−	6.62489i	−0.141275	−	0.244696i	0.786702	−	0.617333i	$-0.211787\pi$
$733$	−3.82488	−	6.62489i	−0.141275	−	0.244696i	−0.927977	+	0.372637i	$0.878454\pi$
$734$	−12.0613	−	20.8908i	−0.445190	−	0.771092i
$735$	2.24770	−	0.732113i	0.0829075	−	0.0270044i
$736$	−8.53085	−	1.50422i	−0.314451	−	0.0554462i
$737$	6.47100	+	2.35525i	0.238362	+	0.0867568i
$738$	−14.3197	−	22.7058i	−0.527114	−	0.835813i
$739$	−2.72684	+	15.4647i	−0.100309	+	0.568878i	0.892682	+	0.450687i	$0.148821\pi$
$739$	−2.72684	+	15.4647i	−0.100309	+	0.568878i	−0.992991	+	0.118192i	$0.962290\pi$
$740$	0.0744072	−	0.128877i	0.00273526	−	0.00473762i
$741$	30.1231	+	20.7669i	1.10660	+	0.762892i
$742$	2.44680	−	6.19923i	0.0898248	−	0.227581i
$743$	−8.27067	−	6.93992i	−0.303422	−	0.254601i	0.478345	−	0.878172i	$-0.341237\pi$
$743$	−8.27067	−	6.93992i	−0.303422	−	0.254601i	−0.781767	+	0.623571i	$0.785681\pi$
$744$	0.789679	+	0.270075i	0.0289510	+	0.00990143i
$745$	0.220583	−	0.185091i	0.00808153	−	0.00678120i
$746$	3.40914	+	9.36654i	0.124818	+	0.342933i
$747$	6.57223	+	16.0743i	0.240465	+	0.588127i
$748$	−18.0067	−	31.1886i	−0.658392	−	1.14037i
$749$	−29.5923	+	4.40209i	−1.08128	+	0.160849i
$750$	1.73867	+	2.88007i	0.0634874	+	0.105165i
$751$	−13.9408	+	2.45814i	−0.508707	+	0.0896988i	−0.422110	−	0.906545i	$-0.638710\pi$
$751$	−13.9408	+	2.45814i	−0.508707	+	0.0896988i	−0.0865971	+	0.996243i	$0.527599\pi$
$752$		−	0.815882i		−	0.0297522i
$753$	−35.9787	−	29.0114i	−1.31114	−	1.05724i
$754$	6.17371	+	7.35754i	0.224833	+	0.267946i
$755$	−0.346232	+	1.96358i	−0.0126007	+	0.0714619i
$756$	−1.95651	+	13.6078i	−0.0711575	+	0.494911i
$757$	28.5696	−	10.3985i	1.03838	−	0.377939i	0.234114	−	0.972209i	$-0.424781\pi$
$757$	28.5696	−	10.3985i	1.03838	−	0.377939i	0.804266	+	0.594270i	$0.202559\pi$
$758$	−12.8404	−	35.2787i	−0.466384	−	1.28138i
$759$	−27.6491	−	71.5837i	−1.00360	−	2.59832i
$760$	−0.495951	+	0.690151i	−0.0179900	+	0.0250344i
$761$	−5.92182	−	3.41897i	−0.214666	−	0.123937i	0.388812	−	0.921317i	$-0.372886\pi$
$761$	−5.92182	−	3.41897i	−0.214666	−	0.123937i	−0.603478	+	0.797380i	$0.706219\pi$
$762$	−7.51539	+	6.56048i	−0.272254	+	0.237661i
$763$	−25.2392	−	46.5601i	−0.913721	−	1.68559i
$764$	16.0262	−	2.82586i	0.579808	−	0.102236i
$765$	2.19703	+	3.48370i	0.0794338	+	0.125953i
$766$	4.09110	+	23.2018i	0.147817	+	0.838314i
$767$	−26.8660	−	15.5111i	−0.970074	−	0.560072i
$768$	0.624069	+	1.61572i	0.0225191	+	0.0583021i
$769$	15.3743	−	12.9006i	0.554412	−	0.465207i	−0.322020	−	0.946733i	$-0.604362\pi$
$769$	15.3743	−	12.9006i	0.554412	−	0.465207i	0.876432	+	0.481526i	$0.159917\pi$
$770$	2.58502	+	0.527755i	0.0931578	+	0.0190190i
$771$	1.80936	−	2.24389i	0.0651626	−	0.0808118i
$772$			1.26423i			0.0455007i
$773$	9.34059	+	52.9731i	0.335958	+	1.90531i	0.417565	+	0.908647i	$0.362884\pi$
$773$	9.34059	+	52.9731i	0.335958	+	1.90531i	−0.0816072	+	0.996665i	$0.526005\pi$
$774$	−19.6295	+	0.767131i	−0.705566	+	0.0275739i
$775$	0.817744	−	2.24673i	0.0293742	−	0.0807051i
$776$	1.40192	+	3.85173i	0.0503259	+	0.138269i
$777$	−1.17216	−	3.29542i	−0.0420511	−	0.118223i
$778$		−	12.9474i		−	0.464185i
$779$	−31.6736	−	22.7611i	−1.13482	−	0.815499i
$780$	0.589665	+	1.52665i	0.0211134	+	0.0546627i
$781$	−60.7186	−	10.7063i	−2.17268	−	0.383102i
$782$	−10.5918	+	60.0688i	−0.378760	+	2.14806i
$783$	2.94948	−	9.86680i	0.105406	−	0.352611i
$784$	−0.843663	−	6.94897i	−0.0301308	−	0.248178i
$785$	−0.984075	+	2.70372i	−0.0351232	+	0.0965001i
$786$	−1.72718	+	11.0535i	−0.0616064	+	0.394266i
$787$		−	5.74712i		−	0.204863i	−0.994740	−	0.102431i	$-0.967338\pi$
$787$		−	5.74712i		−	0.204863i	0.994740	−	0.102431i	$-0.0326622\pi$
$788$	6.68887	−	18.3775i	0.238281	−	0.654672i
$789$	17.0665	−	0.333357i	0.607584	−	0.0118678i
$790$	0.414791	−	0.718440i	0.0147576	−	0.0255609i
$791$	31.4715	−	4.68163i	1.11900	−	0.166460i
$792$	−9.39621	+	12.1301i	−0.333880	+	0.431025i
$793$	31.8011	−	37.8990i	1.12929	−	1.34583i
$794$	9.35197	−	7.84723i	0.331889	−	0.278488i
$795$	−0.640850	+	0.559423i	−0.0227286	+	0.0198407i
$796$	8.45050	−	3.07573i	0.299520	−	0.109016i
$797$	−15.0697			−0.533797			−0.266899	−	0.963725i	$-0.585999\pi$
$797$	−15.0697			−0.533797			−0.266899	+	0.963725i	$0.585999\pi$
$798$	4.79133	+	19.3918i	0.169611	+	0.686463i
$799$	−5.74492			−0.203241
$800$	4.66274	−	1.69710i	0.164853	−	0.0600015i
$801$	1.50821	+	2.39148i	0.0532902	+	0.0844990i
$802$	−14.3071	+	12.0051i	−0.505200	+	0.423914i
$803$	9.99362	−	11.9099i	0.352667	−	0.420293i
$804$	−1.12636	+	2.04200i	−0.0397237	+	0.0720158i
$805$	−2.77935	−	3.49899i	−0.0979593	−	0.123323i
$806$	1.16756	−	2.02227i	0.0411255	−	0.0712315i
$807$	−0.238175	−	12.1936i	−0.00838416	−	0.429234i
$808$	−1.18805	+	3.26415i	−0.0417956	+	0.114833i
$809$		−	21.4310i		−	0.753475i	−0.926320	−	0.376737i	$-0.877046\pi$
$809$		−	21.4310i		−	0.753475i	0.926320	−	0.376737i	$-0.122954\pi$
$810$	1.01959	−	1.42815i	0.0358248	−	0.0501800i
$811$	−16.0110	+	43.9898i	−0.562222	+	1.54469i	0.254151	+	0.967165i	$0.418204\pi$
$811$	−16.0110	+	43.9898i	−0.562222	+	1.54469i	−0.816372	+	0.577526i	$0.804018\pi$
$812$	−0.140815	+	5.24170i	−0.00494165	+	0.183948i
$813$	−0.941784	−	48.2154i	−0.0330298	−	1.69099i
$814$	0.677874	−	3.84442i	0.0237595	−	0.134747i
$815$	1.73479	+	0.305891i	0.0607672	+	0.0107149i
$816$	11.3768	−	4.39430i	0.398269	−	0.153831i
$817$	−26.0142	+	11.7451i	−0.910123	+	0.410907i
$818$			25.1003i			0.877611i
$819$	36.3034	+	12.7139i	1.26854	+	0.444258i
$820$	−0.596698	−	1.63941i	−0.0208376	−	0.0572508i
$821$	2.51896	−	6.92078i	0.0879122	−	0.241537i	−0.887944	−	0.459952i	$-0.847867\pi$
$821$	2.51896	−	6.92078i	0.0879122	−	0.241537i	0.975856	+	0.218415i	$0.0700888\pi$
$822$	−2.73180	−	13.8997i	−0.0952826	−	0.484808i
$823$	−8.76350	−	49.7003i	−0.305476	−	1.73244i	−0.621254	−	0.783609i	$-0.713376\pi$
$823$	−8.76350	−	49.7003i	−0.305476	−	1.73244i	0.315777	−	0.948833i	$-0.397735\pi$
$824$		−	14.0202i		−	0.488415i
$825$	34.2181	+	27.5918i	1.19132	+	0.960623i
$826$	−5.36312	−	16.0649i	−0.186607	−	0.558968i
$827$	20.5119	−	17.2115i	0.713267	−	0.598502i	−0.212247	−	0.977216i	$-0.568078\pi$
$827$	20.5119	−	17.2115i	0.713267	−	0.598502i	0.925514	+	0.378714i	$0.123634\pi$
$828$	25.3968	−	5.50862i	0.882600	−	0.191438i
$829$	37.4129	+	21.6004i	1.29940	+	0.750212i	0.980301	−	0.197508i	$-0.0632849\pi$
$829$	37.4129	+	21.6004i	1.29940	+	0.750212i	0.319104	+	0.947720i	$0.396618\pi$
$830$	0.195985	+	1.11148i	0.00680273	+	0.0385802i
$831$	−21.2602	−	24.3547i	−0.737509	−	0.844857i
$832$	4.77254	−	0.841528i	0.165458	−	0.0291747i
$833$	−48.9303	+	5.94054i	−1.69533	+	0.205827i
$834$	9.91040	+	11.3529i	0.343169	+	0.393119i
$835$	−0.875821	−	0.505656i	−0.0303090	−	0.0174989i
$836$	−6.03329	+	21.4620i	−0.208666	+	0.742277i
$837$	−2.49946	+	0.146614i	−0.0863940	+	0.00506772i
$838$	−1.94868	−	5.35397i	−0.0673162	−	0.184950i
$839$	−0.550877	+	0.200503i	−0.0190184	+	0.00692213i	−0.351512	−	0.936183i	$-0.614332\pi$
$839$	−0.550877	+	0.200503i	−0.0190184	+	0.00692213i	0.332493	+	0.943106i	$0.392110\pi$
$840$	−0.311732	+	0.837334i	−0.0107558	+	0.0288908i
$841$	−4.35372	+	24.6912i	−0.150128	+	0.851421i
$842$	0.787723	+	0.938772i	0.0271467	+	0.0323522i
$843$	−2.50407	+	3.10543i	−0.0862447	+	0.106957i
$844$		−	19.1076i		−	0.657711i
$845$	2.01330	−	0.354999i	0.0692597	−	0.0122124i
$846$	0.926324	+	2.26559i	0.0318477	+	0.0778926i
$847$	39.6697	−	5.90118i	1.36307	−	0.202767i
$848$	1.25950	+	2.18151i	0.0432513	+	0.0749134i
$849$	43.9281	−	26.5190i	1.50761	−	0.910129i
$850$	−11.9499	−	32.8321i	−0.409878	−	1.12613i
$851$	−5.06484	+	4.24990i	−0.173620	+	0.145685i
$852$	6.75672	−	19.7561i	0.231481	−	0.676834i
$853$	−34.4754	−	28.9283i	−1.18042	−	0.990487i	−0.999976	−	0.00690099i	$-0.997803\pi$
$853$	−34.4754	−	28.9283i	−1.18042	−	0.990487i	−0.180440	−	0.983586i	$-0.557752\pi$
$854$	26.7160	−	3.97422i	0.914203	−	0.135995i
$855$	0.593613	−	2.47954i	0.0203011	−	0.0847984i
$856$	5.65395	−	9.79293i	0.193248	−	0.334716i
$857$	4.59719	−	26.0719i	0.157037	−	0.890600i	−0.799863	−	0.600183i	$-0.795095\pi$
$857$	4.59719	−	26.0719i	0.157037	−	0.890600i	0.956900	−	0.290418i	$-0.0937943\pi$
$858$	28.2323	+	32.3416i	0.963834	+	1.10412i
$859$	12.1863	+	4.43543i	0.415790	+	0.151335i	0.541440	−	0.840740i	$-0.317879\pi$
$859$	12.1863	+	4.43543i	0.415790	+	0.151335i	−0.125650	+	0.992075i	$0.540102\pi$
$860$	−1.25732	−	0.221699i	−0.0428741	−	0.00755986i
$861$	−38.4284	−	14.3065i	−1.30964	−	0.487565i
$862$	−6.33100	−	10.9656i	−0.215635	−	0.373490i
$863$	−23.6003	−	40.8770i	−0.803365	−	1.39147i	−0.917389	−	0.397991i	$-0.869708\pi$
$863$	−23.6003	−	40.8770i	−0.803365	−	1.39147i	0.114025	−	0.993478i	$-0.463626\pi$
$864$	−3.56738	−	3.77807i	−0.121365	−	0.128533i
$865$	0.788086	−	2.16525i	0.0267957	−	0.0736206i
$866$	14.1484	−	8.16857i	0.480782	−	0.277579i
$867$	−20.3327	−	52.6413i	−0.690533	−	1.78779i
$868$	1.20925	−	0.403696i	0.0410445	−	0.0137023i
$869$	3.77889	−	21.4311i	0.128190	−	0.727001i
$870$	0.323262	−	0.586048i	0.0109596	−	0.0198689i
$871$	4.99839	+	4.19414i	0.169364	+	0.142113i
$872$	19.7132	+	3.47598i	0.667575	+	0.117711i
$873$	−8.26605	−	9.10404i	−0.279763	−	0.308125i
$874$	31.1930	−	21.2772i	1.05512	−	0.719713i
$875$	4.78004	+	1.88665i	0.161595	+	0.0637805i
$876$	3.46247	+	3.96645i	0.116986	+	0.134014i
$877$	−22.7766	−	4.01612i	−0.769110	−	0.135615i	−0.224693	−	0.974430i	$-0.572138\pi$
$877$	−22.7766	−	4.01612i	−0.769110	−	0.135615i	−0.544417	+	0.838815i	$0.683249\pi$
$878$	−5.48596	−	6.53792i	−0.185142	−	0.220644i
$879$	9.98506	−	1.96243i	0.336788	−	0.0661912i
$880$	−0.763901	+	0.640989i	−0.0257511	+	0.0216077i
$881$	−36.7210	+	21.2009i	−1.23716	+	0.714275i	−0.968513	−	0.248964i	$-0.919910\pi$
$881$	−36.7210	+	21.2009i	−1.23716	+	0.714275i	−0.268648	+	0.963239i	$0.586577\pi$
$882$	10.2324	+	18.3385i	0.344541	+	0.617488i
$883$	−27.9401	+	23.4445i	−0.940259	+	0.788971i	−0.977630	−	0.210331i	$-0.932546\pi$
$883$	−27.9401	+	23.4445i	−0.940259	+	0.788971i	0.0373716	+	0.999301i	$0.488101\pi$
$884$	−5.92551	−	33.6052i	−0.199296	−	1.13027i
$885$	−0.333739	+	2.13585i	−0.0112185	+	0.0717957i
$886$	2.59200	+	1.49649i	0.0870800	+	0.0502756i
$887$	−34.6091	+	29.0405i	−1.16206	+	0.975083i	−0.999932	−	0.0116866i	$-0.996280\pi$
$887$	−34.6091	+	29.0405i	−1.16206	+	0.975083i	−0.162127	+	0.986770i	$0.551835\pi$
$888$	1.25087	+	0.427804i	0.0419763	+	0.0143562i
$889$	−3.04822	+	14.9306i	−0.102234	+	0.500758i
$890$	0.0628470	+	0.172671i	0.00210664	+	0.00578794i
$891$	12.3198	−	44.3518i	0.412730	−	1.48584i
$892$	−16.5026	+	9.52778i	−0.552548	+	0.319014i
$893$	2.48374	+	2.54532i	0.0831152	+	0.0851758i
$894$	1.99129	+	1.60568i	0.0665988	+	0.0537020i
$895$	2.67022	−	3.18224i	0.0892555	−	0.106371i
$896$	2.25494	+	1.38393i	0.0753321	+	0.0462339i
$897$	−1.41998	−	72.6971i	−0.0474118	−	2.42729i
$898$	10.3289	+	8.66694i	0.344678	+	0.289219i
$899$	−0.940463	+	0.165829i	−0.0313662	+	0.00553071i
$900$	−11.0209	+	10.0065i	−0.367365	+	0.333551i
$901$	15.3608	−	8.86857i	0.511743	−	0.295455i
$902$	−29.4174	−	35.0583i	−0.979492	−	1.16731i
$903$	−23.1277	+	19.1194i	−0.769642	+	0.636254i
$904$	−6.01300	+	10.4148i	−0.199989	+	0.346392i
$905$	2.01085			0.0668429
$906$	−17.7092	+	0.345912i	−0.588350	+	0.0114921i
$907$	3.67847	+	10.1065i	0.122142	+	0.335581i	0.985662	−	0.168733i	$-0.0539675\pi$
$907$	3.67847	+	10.1065i	0.122142	+	0.335581i	−0.863520	+	0.504314i	$0.831745\pi$
$908$	16.5282	+	6.01578i	0.548509	+	0.199641i
$909$	−0.406945	−	10.4130i	−0.0134975	−	0.345376i
$910$	2.13063	+	1.30764i	0.0706296	+	0.0433478i
$911$	−13.5003			−0.447286			−0.223643	−	0.974671i	$-0.571795\pi$
$911$	−13.5003			−0.447286			−0.223643	+	0.974671i	$0.571795\pi$
$912$	−6.86554	−	3.14075i	−0.227341	−	0.104001i
$913$	14.8032	+	25.6399i	0.489915	+	0.848557i
$914$	−4.23594	+	24.0232i	−0.140112	+	0.794616i
$915$	−3.26205	−	1.11564i	−0.107840	−	0.0368819i
$916$	−0.779858	−	4.42279i	−0.0257672	−	0.146133i
$917$	8.14417	+	15.0240i	0.268944	+	0.496136i
$918$	−26.6028	+	25.1192i	−0.878022	+	0.829057i
$919$	5.24063			0.172872			0.0864362	−	0.996257i	$-0.472452\pi$
$919$	5.24063			0.172872			0.0864362	+	0.996257i	$0.472452\pi$
$920$	1.68894			0.0556829
$921$	−2.17706	+	3.94682i	−0.0717364	+	0.130052i
$922$	−25.9455	+	4.57490i	−0.854470	+	0.150666i
$923$	−50.5930	−	29.2099i	−1.66529	−	0.961456i
$924$	−0.171742	+	23.4372i	−0.00564990	+	0.771028i
$925$	1.29532	−	3.55887i	0.0425899	−	0.117015i
$926$	23.3116	+	19.5608i	0.766067	+	0.642807i
$927$	15.9180	+	38.9320i	0.522815	+	1.27869i
$928$	−1.51822	−	1.27394i	−0.0498379	−	0.0418190i
$929$	9.36550	+	25.7315i	0.307272	+	0.844223i	0.993186	+	0.116540i	$0.0371804\pi$
$929$	9.36550	+	25.7315i	0.307272	+	0.844223i	−0.685914	+	0.727683i	$0.740597\pi$
$930$	−0.160771	−	0.0251214i	−0.00527189	−	0.000823764i
$931$	23.7863	+	19.1105i	0.779565	+	0.626321i
$932$			10.2429i			0.335517i
$933$	−8.96697	−	45.6249i	−0.293565	−	1.49369i
$934$	15.8603	−	18.9016i	0.518964	−	0.618478i
$935$	4.51344	+	5.37890i	0.147605	+	0.175909i
$936$	−12.2972	+	7.75539i	−0.401948	+	0.253493i
$937$	33.0612	+	12.0333i	1.08006	+	0.393111i	0.819931	−	0.572462i	$-0.194012\pi$
$937$	33.0612	+	12.0333i	1.08006	+	0.393111i	0.260132	+	0.965573i	$0.416234\pi$
$938$	0.524147	+	3.52349i	0.0171140	+	0.115046i
$939$	−8.84668	+	10.9713i	−0.288701	+	0.358033i
$940$	0.0276231	+	0.156658i	0.000900966	+	0.00510963i
$941$	48.8150	+	17.7672i	1.59132	+	0.579194i	0.977627	−	0.210347i	$-0.0674594\pi$
$941$	48.8150	+	17.7672i	1.59132	+	0.579194i	0.613697	+	0.789542i	$0.289682\pi$
$942$	−25.2537	−	3.94604i	−0.822809	−	0.128569i
$943$			77.5120i			2.52414i
$944$	6.01532	+	2.18940i	0.195782	+	0.0712589i
$945$	−0.0850443	−	2.67909i	−0.00276649	−	0.0871507i
$946$	−32.9821	+	5.81563i	−1.07234	+	0.189083i
$947$	26.7761	+	4.72134i	0.870105	+	0.153423i	0.590838	−	0.806790i	$-0.298797\pi$
$947$	26.7761	+	4.72134i	0.870105	+	0.153423i	0.279267	+	0.960213i	$0.409908\pi$
$948$	6.97309	+	2.38484i	0.226476	+	0.0774560i
$949$	12.7578	−	7.36573i	0.414136	−	0.239102i
$950$	−9.38003	+	19.4890i	−0.304329	+	0.632305i
$951$	22.3533	+	3.49283i	0.724854	+	0.113263i
$952$	9.74476	−	15.8778i	0.315829	−	0.514603i
$953$	−19.0368	+	6.92884i	−0.616663	+	0.224447i	−0.631416	−	0.775444i	$-0.717526\pi$
$953$	−19.0368	+	6.92884i	−0.616663	+	0.224447i	0.0147530	+	0.999891i	$0.495304\pi$
$954$	−5.97426	−	4.62776i	−0.193424	−	0.149829i
$955$	−2.98154	+	1.08519i	−0.0964803	+	0.0351159i
$956$	−21.2815	+	3.75250i	−0.688293	+	0.121365i
$957$	2.71049	−	17.3465i	0.0876176	−	0.560731i
$958$	16.3514	+	9.44051i	0.528291	+	0.305009i
$959$	−16.1964	−	14.3490i	−0.523010	−	0.463353i
$960$	−0.174531	−	0.289106i	−0.00563296	−	0.00933087i
$961$	−15.3839	−	26.6457i	−0.496255	−	0.859539i
$962$	1.84944	−	3.20332i	0.0596282	−	0.103279i
$963$	−4.58168	+	33.6129i	−0.147642	+	1.08316i
$964$	−0.133124	+	0.158651i	−0.00428765	+	0.00510982i
$965$	−0.0428028	−	0.242747i	−0.00137787	−	0.00781429i
$966$	25.7385	−	30.2214i	0.828121	−	0.972357i
$967$	−6.19324	−	5.19675i	−0.199161	−	0.167116i	0.537753	−	0.843103i	$-0.319273\pi$
$967$	−6.19324	−	5.19675i	−0.199161	−	0.167116i	−0.736914	+	0.675986i	$0.763718\pi$
$968$	−7.57937	+	13.1279i	−0.243610	+	0.421945i
$969$	−22.1152	+	48.3428i	−0.710442	+	1.55299i
$970$	−0.399590	−	0.692111i	−0.0128301	−	0.0222223i
$971$	47.0639	−	17.1299i	1.51035	−	0.549724i	0.551637	−	0.834085i	$-0.314004\pi$
$971$	47.0639	−	17.1299i	1.51035	−	0.549724i	0.958717	+	0.284361i	$0.0917813\pi$
$972$	14.1956	+	6.44089i	0.455324	+	0.206592i
$973$	22.5545	+	4.60470i	0.723065	+	0.147620i
$974$	24.2217	+	4.27093i	0.776112	+	0.136850i
$975$	21.5254	+	35.6564i	0.689365	+	1.14192i
$976$	−5.10441	+	8.84110i	−0.163388	+	0.282997i
$977$	−1.11026			−0.0355203			−0.0177601	−	0.999842i	$-0.505654\pi$
$977$	−1.11026			−0.0355203			−0.0177601	+	0.999842i	$0.505654\pi$
$978$	0.305608	+	15.6459i	0.00977227	+	0.500299i
$979$	3.09838	+	3.69250i	0.0990246	+	0.118013i
$980$	0.397262	+	1.30572i	0.0126901	+	0.0417096i
$981$	−58.6874	+	12.7294i	−1.87374	+	0.406419i
$982$	4.39883	+	5.24232i	0.140372	+	0.167289i
$983$	28.4424	−	10.3522i	0.907172	−	0.330184i	0.154049	−	0.988063i	$-0.450769\pi$
$983$	28.4424	−	10.3522i	0.907172	−	0.330184i	0.753123	+	0.657879i	$0.228546\pi$
$984$	13.2682	−	8.00988i	0.422974	−	0.255346i
$985$	−0.662134	+	3.75515i	−0.0210973	+	0.119649i
$986$	−8.97025	+	10.6903i	−0.285671	+	0.340449i
$987$	3.22415	+	1.89310i	0.102626	+	0.0602579i
$988$	−12.3272	+	17.1541i	−0.392179	+	0.545744i
$989$	49.1236	+	28.3615i	1.56204	+	0.901843i
$990$	1.39349	−	2.64724i	0.0442880	−	0.0841349i
$991$	−14.3266	+	17.0738i	−0.455100	+	0.542366i	−0.943988	−	0.329980i	$-0.892958\pi$
$991$	−14.3266	+	17.0738i	−0.455100	+	0.542366i	0.488888	+	0.872346i	$0.337402\pi$
$992$	−0.164802	+	0.452789i	−0.00523246	+	0.0143761i
$993$	−45.2590	−	15.4788i	−1.43625	−	0.491206i
$994$	−10.0996	−	30.2528i	−0.320341	−	0.959561i
$995$	−1.51845	+	0.876680i	−0.0481382	+	0.0277926i
$996$	−9.35282	+	3.61252i	−0.296355	+	0.114467i
$997$	−14.4787	−	5.26982i	−0.458545	−	0.166897i	0.102411	−	0.994742i	$-0.467344\pi$
$997$	−14.4787	−	5.26982i	−0.458545	−	0.166897i	−0.560956	+	0.827845i	$0.689567\pi$
$998$	−25.7234	−	9.36256i	−0.814261	−	0.296367i
$999$	−3.95919	+	0.232239i	−0.125263	+	0.00734772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bu.b.611.7	yes	162
3.2	odd	2		798.2.bu.a.611.21	yes	162
7.4	even	3		798.2.cc.b.725.12	yes	162
19.13	odd	18		798.2.cc.a.317.15	yes	162
21.11	odd	6		798.2.cc.a.725.15	yes	162
57.32	even	18		798.2.cc.b.317.12	yes	162
133.32	odd	18		798.2.bu.a.431.21	✓	162
399.32	even	18	inner	798.2.bu.b.431.7	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.431.21	✓	162	133.32	odd	18
798.2.bu.a.611.21	yes	162	3.2	odd	2
798.2.bu.b.431.7	yes	162	399.32	even	18	inner
798.2.bu.b.611.7	yes	162	1.1	even	1	trivial
798.2.cc.a.317.15	yes	162	19.13	odd	18
798.2.cc.a.725.15	yes	162	21.11	odd	6
798.2.cc.b.317.12	yes	162	57.32	even	18
798.2.cc.b.725.12	yes	162	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bu (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.13904 - 1.30483i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.125326 + 0.149358i) q^{5} +(-1.51663 - 0.836567i) q^{6} +(-2.61695 + 0.389293i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.405175 + 2.97251i) q^{9} +(-0.0666847 + 0.183215i) q^{10} +5.11456i q^{11} +(-1.71129 - 0.267399i) q^{12} +(-1.65749 + 4.55391i) q^{13} +(-2.32599 + 1.26087i) q^{14} +(0.337639 - 0.00659504i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-6.93439 - 1.22272i) q^{17} +(0.635920 + 2.93183i) q^{18} +(2.45626 + 3.60094i) q^{19} +0.194973i q^{20} +(3.48878 + 2.97127i) q^{21} +(1.74928 + 4.80612i) q^{22} +(2.96273 - 8.14004i) q^{23} +(-1.69954 + 0.334022i) q^{24} +(0.861640 + 4.88660i) q^{25} +4.84617i q^{26} +(4.34014 - 2.85713i) q^{27} +(-1.75447 + 1.98036i) q^{28} +(1.51822 - 1.27394i) q^{29} +(0.315021 - 0.121677i) q^{30} +(-0.417293 - 0.240924i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(6.67364 - 5.82569i) q^{33} +(-6.93439 + 1.22272i) q^{34} +(0.269829 - 0.439652i) q^{35} +(1.60031 + 2.53752i) q^{36} +(-0.661000 - 0.381628i) q^{37} +(3.53972 + 2.54369i) q^{38} +(7.83003 - 3.02434i) q^{39} +(0.0666847 + 0.183215i) q^{40} +(-8.40841 + 3.06041i) q^{41} +(4.29461 + 1.59885i) q^{42} +(-1.13707 + 6.44867i) q^{43} +(3.28758 + 3.91798i) q^{44} +(-0.393190 - 0.433050i) q^{45} -8.66245i q^{46} +(0.803487 - 0.141676i) q^{47} +(-1.48280 + 0.895154i) q^{48} +(6.69690 - 2.03752i) q^{49} +(2.48099 + 4.29721i) q^{50} +(6.30310 + 10.4409i) q^{51} +(1.65749 + 4.55391i) q^{52} +(-1.92966 + 1.61918i) q^{53} +(3.10120 - 4.16924i) q^{54} +(-0.763901 - 0.640989i) q^{55} +(-0.971340 + 2.46100i) q^{56} +(1.90085 - 7.30663i) q^{57} +(0.990946 - 1.71637i) q^{58} +(-1.11159 + 6.30412i) q^{59} +(0.254407 - 0.222082i) q^{60} +(-9.59315 - 3.49162i) q^{61} +(-0.474528 - 0.0836721i) q^{62} +(-0.0968538 - 7.93666i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.472436 - 0.818283i) q^{65} +(4.27867 - 7.75688i) q^{66} +(0.460499 - 1.26521i) q^{67} +(-6.09800 + 3.52068i) q^{68} +(-13.9961 + 5.40597i) q^{69} +(0.103187 - 0.505425i) q^{70} +(-2.09330 + 11.8717i) q^{71} +(2.37168 + 1.83715i) q^{72} +(-2.32863 - 1.95396i) q^{73} +(-0.751661 - 0.132538i) q^{74} +(5.39475 - 6.69033i) q^{75} +(4.19625 + 1.17963i) q^{76} +(-1.99106 - 13.3846i) q^{77} +(6.32344 - 5.51998i) q^{78} +(-4.19022 - 0.738849i) q^{79} +(0.125326 + 0.149358i) q^{80} +(-8.67167 - 2.40877i) q^{81} +(-6.85460 + 5.75169i) q^{82} +(5.01312 - 2.89433i) q^{83} +(4.58245 + 0.0335791i) q^{84} +(1.05168 - 0.882468i) q^{85} +(1.13707 + 6.44867i) q^{86} +(-3.39158 - 0.529955i) q^{87} +(4.42934 + 2.55728i) q^{88} +(0.721959 - 0.605795i) q^{89} +(-0.517589 - 0.272455i) q^{90} +(2.56477 - 12.5626i) q^{91} +(-2.96273 - 8.14004i) q^{92} +(0.160948 + 0.818920i) q^{93} +(0.706575 - 0.407941i) q^{94} +(-0.845663 - 0.0844309i) q^{95} +(-1.08722 + 1.34832i) q^{96} +(-2.63474 + 3.13996i) q^{97} +(5.59616 - 4.20512i) q^{98} +(-15.2031 - 2.07229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 81 q^{8} + 15 q^{13} - 6 q^{14} + 3 q^{15} + 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} + 9 q^{27} + 9 q^{28} - 6 q^{29} + 24 q^{33} + 6 q^{34} - 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots + 39 q^{99}+O(q^{100}) \) 162 * q + 81 * q^8 + 15 * q^13 - 6 * q^14 + 3 * q^15 + 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 + 9 * q^27 + 9 * q^28 - 6 * q^29 + 24 * q^33 + 6 * q^34 - 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 + 12 * q^44 + 45 * q^45 - 12 * q^47 - 48 * q^49 - 87 * q^50 + 24 * q^51 - 15 * q^52 + 18 * q^54 - 18 * q^57 + 48 * q^59 + 18 * q^60 + 45 * q^61 - 36 * q^62 - 21 * q^63 - 81 * q^64 - 36 * q^65 + 12 * q^66 + 9 * q^67 - 9 * q^69 - 24 * q^70 - 12 * q^71 + 102 * q^73 - 39 * q^74 - 18 * q^78 - 42 * q^79 - 12 * q^81 + 57 * q^84 - 6 * q^85 + 9 * q^86 + 60 * q^87 - 54 * q^89 + 12 * q^90 - 18 * q^91 + 105 * q^93 - 72 * q^94 - 12 * q^97 + 27 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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